The decision rule.

In our experimental approach to the concept of personal identity we are guided by Robert Nozick’s [14] closest continuer theory, which allows us to connect debates in metaphysics on personal identity with several strands of research on identity in psychology. Nozick [14] offered a systematic approach to adjudicating between identity claims, which he called the “closest continuer view” (p. 34). The central claim is that if x is an object or a person at t₁, then “something at t₂ is not the same entity as x at t₂ if it is not x’s closest continuer” (p. 34); Nozick added that being the closest continuer was a necessary, but not a sufficient, condition. Some details need to be fleshed out, and for this purpose the decision procedure for determining whether an object continues to exist at t₂ or not is illustrated in Fig 1 as a fast-and-frugal decision tree [35]. Continuers of an object x are named y₁, y₂, …, y_k and refer to the set of persons or objects with any form of claim to be the same object or person at t₂ as x at t₁. The branches of the tree correspond to four different cases of interests, each with one of two decision outcomes.

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Fig 1. Decision tree to determine the state of a person or object x that exists at t₁: Y_i is a possible continuer i of x at t₂ (adapted from Nozick, 1981).

https://doi.org/10.1371/journal.pone.0228271.g001

If nothing at t₂ even qualifies to be a continuer of an object, then nothing at t₂ will be identical to x and x cannot exist at t₂ (Case 1). This is the first decision in the tree and possibly the simplest outcome. In the puzzle scenario of the Greek vessel introduced above, both the repaired and reconstructed ship are continuers of the original. Nozick argued that further decision steps depend on a metric of “closeness” to the original x, an intentionally vague term that will be further analyzed below. A second step tests whether there is any continuer that is close enough to qualify as being identical with x. If the ship catches fire and turns into ash at the same time that a swarm of fish happens to follow the ship’s planned trajectory, no observer would identify the fish as the original ship; if this is the only possible continuer, the ship would cease to exist (Case 2). But both the repaired and the reconstructed ship could qualify as being close enough, so in this case a third question is required: Is there a single closest continuer at t₂? In the classic fission scenario [6], a person is copied particle by particle so that two persons are qualitatively identical and have more or less symmetric claims to be the original person. Determining whether there is in fact a closest continuer in this case requires a closeness measure and an ordinal relation defined over the set of its possible values. Small differences may matter, such as whether one of the continuers was a model for the other or whether one of them was created earlier than the other, which could be enough to determine a closest continuer (Case 4). If there is no such difference, or the differences are considered too trivial. Nozick [14] allowed for a semiorder [36] in conceding the perspective that a closest continuer “must decisively beat out the competition” (p. 40). Nozick would argue that it is “most plausible” (p. 63) to assume that the original no longer exists (Case 3): “If two things at t₂ tie in closeness to x at t₁, then neither is the same entity as x” (see [14], p. 34). Hobbes [25] called the solution of having two numerically identical ships most absurd (“et habuissemus duas naves easdem numero; quod est absurdissimum”, p. 107); the existence of two numerically identical persons at the same time would likewise violate the transitivity of the identity relation.

The closeness metric.

The closest continuer view is intentionally formulated without a predefined metric of closeness, which gives it the character of a metatheory. Very different metaphysical approaches to identity could be reflected by the choice of different metrics. Closeness can come in degrees and therefore should not be conflated with numerical identity [5, 16, 37, 38]. While continuers are compared on a single dimension, Nozick conceives of this as a weighted additive model derived from multiple dimensions [17]. Notably, the metric chosen must reflect the type of entity that is compared—ships might be treated differently than stones, mountains, tennis rackets, and so on. Closeness does not reduce to mere similarity either, as causal knowledge can be invoked to disqualify continuers (see also [23]). While the identity of objects and persons both refer to sameness and continuity, first-person judgments of personal identity have implications for the judge who would not accept an arbitrary decision about what counts as herself (see [14], p. 34).

Instead of following “expert” opinions, Nozick argued that people “judge problem cases in accordance with the dimensions and weighting embodied in their own view of themselves” (p. 105). Whether this is considered inevitable or misguided depends on one’s answer to the question of whether there is a (metaphysically) correct view and correct weighting of dimensions and criteria. If so, variance from this one true view would indicate erroneous or at least ill-informed thinking. Nozick took a different stance, embracing the assumed variability of closeness metrics as expressing variability of what identity is for different persons:

I suggest that there is not simply one correct measure of closeness for persons. Each person’s own selection and weighting of dimensions enter into determining his own actual identity, not merely into his view of it. Because of our differing notions of closeness, for the same structural description of a problem case we can give different answers about which resulting person would be us, each answer correct.

(in [14], p. 106)

On this view, an empirical analysis of folk intuitions of closeness and personal identity is a crucial complement to metaphysical speculation. For related reasons, Mori [39] concluded that “a good enough definition of what personal identity in fact is may be provided by the way it is generally perceived, statistically speaking” (p. 278). Livengood and Machery [40] warned about the danger of philosophers assuming that their own intuitions can safely be ascribed to everybody else and suggest that “rather than guess from the comfort of your armchair, you ought to go out and check” (p. 126) whether decisions coincide or not [26]. Of course, potential variance in choosing and applying criteria might again be related to other individual differences [41, 42]. A good starting point for identifying a subjective closeness metric’s dimensions is the concept people have of themselves, since changes to prominent aspects of one’s self should impact the assessment of closeness between former and present self. Psychology has a long tradition of offering characterizations of what people regard as their self. William James [13] offered a rich definition, which serves as our starting point for investigating dimensions of closeness:

In its widest possible sense, however, a man’s Self is the sum total of all that he CAN call his, not only his body and his psychic powers, but his clothes and his house, his wife and children, his ancestors and friends, his reputation and works, his lands, and yacht and bank-account. All these things give him the same emotions. If they wax and prosper, he feels triumphant; if they dwindle and die away, he feels cast down, —not necessarily in the same degree for each thing, but in much the same way for all.

(p. 193)

Persons thus relate to themselves as comprised of “psychic powers,” or psychology and memories; relations to other people; body; and possessions. The experiments we present study how participants sampled from the general population weight these dimensions of closeness to solve puzzle cases.

Closeness, caring and survival.

Nozick suggested that the metric of continuer closeness was correlated with caring for the continuer. A metric of closeness features in a stream of psychological and economic research on the “future self” [43] that refers to it as connectedness and continuity, but often measures it with a single item, a choice between different visualizations of the predicted overlap between the present and the future self (10 years later). In these scenarios, only one continuer is assumed to exist in the future, but consistent with Nozick’s suggestion, studies found perceived closeness to the future self to be correlated with reduced temporal discounting in experiments [43, 44] and more real-world financial savings [45], as well as a decrease in both cheating and the approval of unethical behavior [46]. Similarly, anticipated changes to the self were found to increase the tendency to expedite rewards and delay burdens [47], as well as to increase charitable “selfless” giving [48]. In all these cases, however, only a single continuer is assumed to exist, which eliminates Case 3 as possible result from the decision heuristic. Changes in closeness to a single continuer only threaten identity if the decrease in closeness could reduce it below the threshold.

In a scenario with multiple continuers, however, Nozick argued that we should care about non-closest continuers “proportionally to their degree of closeness” (p. 64) and care disproportionately for our closest continuer. Molouki [49] provided positive evidence for this assumption by comparing allocation to others and the future self:

Despite the finding that changes in the characteristics of liking, similarity, need, and deservingness seem to have a similar impact on resource allocations to others and to future selves, we nevertheless found a strong “premium” in future-self allocations that cannot be ignored.

(p. 71)

When a person splits into two qualitatively identical persons, it is reasonable to argue that the original person is not numerically identical to either successor. On the other hand, it is not clear that the original person has died or did not survive the process, as either successor alone would seem to continue the life of the original. This opens the possibility that survival and personal identity might come apart after fission. Most philosophers would also agree that a minimum degree of closeness is also invoked in survival [6]. In the special case of multiple closest continuers, the present self may be psychologically connected to multiple identical future copies, at the same time. Each of these connections might even be based on the “right kind” of cause (and not based on pure coincidence or spurious connections). Parfit [6] referred to this relation (psychological connectedness with the right kind of cause) as “Relation R” (p. 262) and believed with others (e.g., [10, 50, 51]) that not identity but Relation R mattered in survival. He assumed both relations to be aligned in ordinary cases, but argued that only identity was constrained by transitivity. There is no contradiction of someone being close to one and only one of two persons that are close to each other, just as it is possible for the eye to distinguish a specific color from one and only one of two other colors that are as a pair indistinguishable to the human eye [36]. Faced with two closest continuers, I cannot be identical to either one, on many accounts, but I might still survive [6, 10, 50, 51]. I would be entitled (before fission occurs) to care for these continuers but mistaken in regarding either or both of them as myself.

Survival should not be confused with mere existence; it is not enough that there are continuers. Non-survival could be regarded as corresponding to Cases 1 and 2 in Nozick’s decision scheme: If there are no continuers, or there is no continuer close enough (above a necessary threshold that may or may not coincide with the one used for identity assessments) then the person does not survive. A second focus of our empirical investigation is therefore to find out how participants resolve these tensions between identity, closeness, and survival. We will now describe the scenario used in our experiments and develop our research questions and hypotheses.

Dimensions of assessing closeness.

The closeness metric is the centerpiece of Nozick’s closest continuer theory. This metric reflects which dimensions with which weight determine decisions between continuers in cases of conflict. It therefore specifies what exactly people refer to as their future selves and reflects what people deem to be their essential parts and how they judge connectedness over time. Here we address an open question in the theory, namely what subcomponents with which relative weights are part of the subjective similarity metric (see [14], p. 69). In the following, we explain our choice of features and develop hypotheses regarding the monetary allocation task in Study 1. Each feature is discussed in turn. Note that our design allows for each feature to receive a positive weight in decision making about allocations, even if splitting positively evaluated components can create conflicts in specific scenarios. Note that we do not derive these features from Nozick’s theory, as the closeness metric could accommodate all or none of them. Thus, our hypotheses are derived from the cited theories in philosophy and psychology.

Body and appearance.

Body and appearance are the most visible attributes of a person. If the primary concern is one of spatiotemporal continuity, changes in shape and form endanger both survival and identity. In addition, a person spending substantial time on their body and appearance (such as body-builders) will likely consider the result of their work an essential part of their self. The continuation of the body seems to be an obvious place to look for personal continuity. A reductionist would see any other feature of a person as entirely dependent on the body. Animalism [62] holds that each human is numerically identical to one animal in one body; the brain is treated as only one organ among many. Yet the strict body criterion has fallen into disrespect with most modern philosophers [11], even when embodied approaches regard mental life as severely dependent on the physical body [63]. Also, tracking people based on visual appearance only has been proven unreliable [1]—think of the multiple villagers who confirmed that du Tilh was Guerre. On the other hand, participants might not share this perspective, and Meyer and colleagues [64] show that participants on Mechanical Turk expressed the belief that mere transplants of body parts might confer non-bodily aspects of the donor. We therefore hypothesized that participants would view their body and appearance as important in determining which of the two continuers deserves compensation, and—ceteris paribus—would allocate more money to the continuer that inherited their body as opposed to the continuer with a randomly selected body. This hypothesis corresponds to expecting a main effect for the inheritance of the original body across scenarios:

Hypothesis 1a Participants will allocate more money to the continuer inheriting their body and appearance.

Personality and psychology.

People’s personality and psychology are a central part of how they behave and react to the world. In a sense, “personality” is what makes a person different from or similar to others. In prominent theories of personal identity, psychological factors are considered the most important criterion for reidentification [12, 15] or self-persistence [31]. [65] demonstrated that participants rated a loss of moral attributes as having a larger impact on perceived change than a loss of other personal attributes. Parfit [6] and Campbell [66] stressed that what matters in survival is psychological connectedness between former and future self, which led us to the following hypothesis:

Hypothesis 1b Participants will allocate more money to the continuer inheriting their personality and psychology.

Memory and knowledge.

Memory and knowledge are central components situating a person in the environment and linking their present state to a personal past. Since Locke [9], autobiographic memory has been considered a key part of how people make sense of or even construct their own self-reference [67], which is equated by some with a psychological notion of identity. Knowledge, on the other hand, includes items in memory that are functional in making people succeed in their endeavors. Like body shape and appearance, knowledge can be the result of intentional care and self-modification. Transhumanists consider the possibility of uploading the “contents of the brain to a different, more flexible medium” (in [68], p. 74) as a way of prolonging a person’s existence. Memory and knowledge are of premium importance in any information-theoretic or cognitive-agent perspective on humans. It should be stressed that not all memories seem to be descriptively accurate and related to objective matters of fact. Therefore, it should not be considered a “logical truth” [69] that an act of remembering an event necessarily involves having witnessed it. Indeed, empirical studies on episodic memory demonstrate remembering to be more than “a simple connection between discrete moments of consciousness” [70]. Children faced with staged duplication scenarios of hamsters [71] assumed that fewer mental than bodily properties would be conferred to the copy; stressing the identity of the original hamster by naming it further decreased children’s expectations that a hamster’s episodic memories would be transferred to its copies. The importance of memory for identity might be enhanced by the role of “signature stories” [72] that acquire self-defining functions (see [73]). In this view, memory is understood as more than a passive, digital storage facility [72], as stories that are told and retold can be reinterpreted in self-narration [74]. Some authors refer to identity based on self-narration as “narrative identity” [32], as opposed to numerical identity. Memories and knowledge about the self appear to have a privileged status: They tend to be better protected in semantic dementia than other types of memories [20]. The following hypothesis reflects the privileged nature of memory as a basis for identity:

Hypothesis 1c Participants will allocate more money to the continuer inheriting their memory and knowledge.

Friends.

Sociological and social-psychological theories of the self and the person [75–78] emphasize interactions and relationships. If a person’s place in society is shaped by social responses, claims, responsibilities, and roles, then their personal identity cannot be easily separated from the identities of people with whom they are socially connected. [79] argued that “[a] person has identity only in relation to other people and other roles” (p. 49). Participants in a study by [15] spontaneously generated terms describing linkages to others when asked to list characteristics of persons. Many social psychologists treat people’s identification with groups and self-categorizations in terms of social categories [80]. These categories are validated by others [81] and play a prominent part in constructing the self [82]. If the self is shaped by the eye or the mere existence of the beholder, a change in the social setting (e.g., replacement of all friends, as close and self-selected components of the personal social network) can be expected to have a major impact on identity.

Participants in our experiments may have been exposed to multiple discourses about identity. According to Davis [83] (p. 373), social psychologists contrast the concepts of (potentially multiple) social identities with the notion of personal identity as “an individual’s identity apart from others,” whereas philosophers view personal identity as numerical identity. It is still worth exploring whether participants consider the continuity (or the continuous evolution) of the personal network as a criterion to determine identity between persons in the scenario. After all, they might share the intuitions of social psychologists [80] more than those of philosophers, who put less emphasis on social roles. When imagining possible future selves, participants from different cultures focused not only on abstract self-improvement, but also on future social relations [84]. Considering the continuity of social relations as a criterion for personal identity led us to the following prediction:

Hypothesis 1d Participants will allocate more money to the continuer inheriting their friends.

Possessions.

Finally, several theories address the interaction between internal human processes and outside objects. These theories raise the possibility that classic boundaries and distinctions might be mistaken, or at least lacking in precision. From the extended mind perspective [85], internal cognitive processes can interact with external structures and processes to extend the boundaries of cognitive systems [86]. For example, if someone relies on technological support to maintain memories and organize their intake of new information, that technology becomes intermeshed with their internal faculties.

Following from [13], marketing scientists have transferred a related concept of extension to the notion of an “extended self” [87]. In an analysis of personal self-concepts derived from James’s list of features of the self, Prelinger [88] found that “possessions and productions” were ranked as less central than body or psychological and personally identifying characteristics, but as more central than the external environment or other people. Referring to these results, the extended self approach [87] considers consumers to literally be what they possess, with a potential for self-extension through control over those objects. Diesendruck and Perez [89] observed that even children do not clearly separate objects from the moral qualities of their owner and may interpret objects as “physical manifestations” of a person’s characteristics: “we become the objects that we own” (p. 11). People’s experiences of themselves and their day-to-day lives becomes interlinked with the objects they own: They actively use objects and brands to construct and clarify who they are [90, 91], and losing or replacing possessions can impact their perception of themselves. From this point of view, possessions are “intimately tied to [a person’s] sense of self” (in [92], p. 550). LeBarr and Shedden [93] recently demonstrated that induced ownership leads new owners of objects to form associations between the owned objects and self within minutes.

Possessions play a defining role in a person’s sense of self and personal identity. This could stem either from the fact that people’s cognitive processes rely on outside objects (e.g., external storage or tailored aids), or from the significance those objects have acquired in defining who the person is. People might therefore consider the continuity of possessions in determining identity. We therefore formulated the following prediction:

Hypothesis 1e Participants will allocate more money to the continuer inheriting their possessions.

In theory, all five hypotheses could be true at the same time, this would correspond to five main effects across all scenarios, in which all possible combinations of original features are explored.

Monetary allocation and personal reidentification.

The questions concerning the state of the original person after fission allow us to study participants’ decision making regarding the consequence for personal identity and survival. We assume that the allocation of money tracks personal reidentification and not other-regarding concerns. We ask two questions in the post-questionnaire of the form “You are person X after the incident” (all questions are listed in S1 Supporting Information) and expect that answers to these questions will respond to scenario conditions in the same way as monetary allocations:

Hypothesis 2 Participants’ personal reidentification with either continuer will follow the same pattern across conditions as the monetary allocation.

Explicit weighting of dimensions.

The weighting of dimensions is assumed by Nozick [14] to be an implicit process. Participants might therefore not have access to the exact weights that would make it possible to predict their decision (and decisions in all other possible scenarios). Nonetheless, it seems plausible to assume that participants can identify important and less important dimensions. When asked about the importance of the five dimensions (body and appearance, personality and psychology, memory and knowledge, friends, possessions) for determining the identity between persons, participants’ weightings should on average correspond to the identified importance for allocation decisions. Asking for the identity “between people” ensures that participants do not answer the question with one of the divergent nonrelational meanings of personal identity commonly used in psychology in mind (see also the General Discussion).

Hypothesis 3 Participants’ subjectively assessed importance of dimensions will correspond to the importance of factors for the allocation decision.

It has been argued that the closeness metric drives reidentification decisions in the fission case. As discussed above, Parfit [6] and others claimed that it is not the identity relation that matters in survival. Rather, he proposed that what matters is Relation R—psychological connectedness and the right kind of continuity—meaning that hypothetically, there can be cases of survival without the preservation of identity. But if connectedness plays a central role for survival judgments, then intuitions about survival should be influenced by a closeness metric, but not necessarily the same metric as identity judgments. To test whether the same or different weights are applied, we also asked participants to assess the importance of the five dimensions in determining whether a person survives. As we do not have a strong prediction, we formulate this as a research question:

Research Question 1 Is the importance assigned to the five dimensions the same for determining survival and the identity between people?

Philosophers differ in the degree of interindividual variance they would expect in the perceived weight of dimensions. While Nozick [14] entitles observers to idiosyncratic weighting, others argue for universally shared intuitions or at least universally shared normatively correct intuitions that should also constrain variations in weights.

Personal reidentification after fission.

Following Nozicks’s [14] decision scheme, our scenarios might correspond to one of three cases for each participant (assuming that the two people after the incident qualify as continuers). Neither continuer can be close enough (Case 2), one can be close enough and closer than the other (Case 4), or both can be close enough but appear too similar to decide between them (Case 3). Case 3 can occur even if continuers in our scenario are never identical. The questions asked after the main task allow us to gain more insight into the decision-making process and the reasoning behind the allocation decision. Of course, no empirical finding could be interpreted as a refutation of Nozick’s normative theory. The analysis will thus focus on the usefulness of this framework for organizing empirical responses by (mostly) non-philosophers. Thus, we formulate research questions, and not hypotheses. In a first step, answers to the open question about reasons for the allocation will be analyzed for correspondence with the closest continuer theory:

Research Question 2 Is there evidence in open answers for participants following the logic of the closest continuer theory?

There is near-universal agreement in philosophy that declaring two distinct continuers to be the same person as the original is inconsistent and clashes with the assumed transitivity of identity. In experiments with non-philosophers, however, psychologists have found evidence for violations of transitivity in people’s assessment of identity relations. Rips and colleagues [17] found that faced with two continuers of animals made up of particles from the original, most participants saw both of them simultaneously as the original, with similar results for objects such as possible continuers of icebergs. The authors excluded simple explanations due to response formats, and Rips [33] replicated these results under several variations. Weaver and Turri [52] claim to be the first to show that these results extend to judgments about the identity of persons. Specifically, they demonstrate that participants violate the “one-person-one-place” rule (p. 34) after a transporter incident duplicates the traveler and locates the person in two places at once in several variations of the scenario. The authors wonder whether “perhaps drastic psychological change across co-located figures could lead people to judge that the figures […] are different persons.” (p. 35). Our scenario allows us to explore this question by analyzing the frequency of participants affirming that they are two people after the incident and the conditions under which these responses are made:

Research Question 3 Are there conditions under which participants consider the original person to be two persons after the incident?

If reidentification judgments are determined by a single dimension, existence should be guaranteed under all scenarios, as all original dimensions are present in one of the two continuers after the incident. If the persistence of two or more dimensions is considered to be necessary for survival, then splitting these dimensions would result in a loss of existence. The closest continuer scheme would predict nonexistence responses in cases where no single continuer is close enough. In this scheme, nonexistence is also predicted if two dimensions are separately sufficient for continuity but both continuers are too similar in closeness. We therefore include a final research question:

Research Question 4 Are there participants who consider the original person to be nonexistent after fission?

Again, the same scenario might be interpreted in different ways by different groups of participants and we will investigate both stability and minority perspectives.

Experimental setting and sample.

Participants were recruited via Amazon Mechanical Turk. Our personal identity questionnaire was embedded in a Human Intelligence Task (HIT) containing a series of cognitive and evaluation tasks lasting an expected 45–60 minutes. Participants were recruited for this task over a period of about 100 hours. A minimum approval-rating filter [94] of 95% was combined with attention-check questions at the beginning of the survey to ensure sufficient attention to questions and instructions. We report on all participants who passed these checks and described themselves as U.S. citizens. Data collection was not restricted to U.S citizens, as other parts of the survey—data supporting [95]—required a broader sample, but a large majority (75.8%) of the respondents were Americans (which is typical for MTurk; see [96]). U.S. participants are the largest group of workers on the Mechanical Turk platform. They are regarded as less representative of the population than national probability samples but as more representative than students or convenience samples [96, 97]. There were 196 responses from India and 29 from other countries. Both samples were too small for separate analysis and—relevant to the complex scenario used in our experiment—there were concerns about the English comprehension and data quality of Indian participants [98, 99].

A total of N = 704 responses were analyzed in Study 1. The mean participant age was 33.4 years (SD = 10.7 years) and 49.7% of participants were female. Participants who completed the survey were remunerated with a fixed payment of $2.50 and a variable bonus of up to $1.50, contingent on their performance in the HIT. Our survey was always embedded at the same position within the HIT. The survey was coded and conducted using the Qualtrics platform. The study received IRB approval (HEC Lausanne Ethics Committee), and participants gave electronic consent after reading a consent form prior to beginning the study.

Experimental design.

We recruited a large sample of participants in a five-factorial between-subjects design with single scenarios to avoid potential order effects [100]. Each participant was exposed to one of 32 variants of the scenario that were created by the 2⁵ possible distributions of the five features between the two resulting persons. The 32 scenario variants in the 2 × 2 × 2 × 2 × 2 between-subjects factorial design were identical, with the exception of the diagram shown to illustrate the division of attributes after the accident (see Fig 2). This complete five-factorial design balances out any positional preference, as each split between the two persons recurs with the positions reversed. In addition, any preference for equal splitting that disregards personal attributes should be expressed equally in all conditions without distorting the results. Each participant was presented one variant of the scenario. We thus obtained independent data for 32 variants differing the allocation of the five features to the two resulting persons. Having read the scenario description, participants were asked 18 questions on the scenario. First, they were instructed to distribute a sum of $100,000 in insurance money between the two resulting persons using two sliders with a fixed-sum constraint. They were then asked to explain their choice of distribution in an open-answer format. Next, participants responded to a series of statements regarding identity and survival after the accident on a continuous slider scale (from “strongly disagree” to “strongly agree”). Finally, they judged the importance of the five features separately, once for the determination of identity, and once for the determination of survival, on a similar continuous scale (from “not at all important” to “extremely important”).

Allocation of insurance money.

Allocations to person A and person B spanned the full possible range (see Fig F in S1 Supporting Information). The mode of the distribution was an equal split between A and B, with other participants choosing amounts very close to $50,000. Few participants chose extreme splits; more respondents chose values around multiples of $10,000. We computed an ANOVA with five between-subjects factors (presence/absence of the five original features in person B) and the insurance money allocation to person B as criterion (see Table A in S1 Supporting Information, for the complete results). All possible interaction terms were included in the model. Cell counts varied from 15 to 30, with a mean of 22.0 participants (SD = 3.5). For the results presented below, the combined dimensions psychology/personality, memory/knowledge, and body/appearance will be referenced as psychology, memory, and body, respectively.

We found two significant main effects: for psychology (F(1, 672) = 45.01, p < .001, partial η² = .06) and memory (F(1, 672) = 45.20, p < .001, partial η² = .06). None of the other main effects were significant; neither were any of the 26 interactions. The two main effects remained significant after Bonferroni correction for the family-wise error rate. In addition, these effects appeared to be robust across all possible distributions of the other three components (see section 2.1.2. in S1 Supporting Information). Our findings on the allocation of insurance money thus support Hypothesis 1b and Hypothesis 1c (participants allocated more money to the continuer inheriting their psychology and personality, and their memories and knowledge). There was little or no support for Hypothesis 1a (body and appearance), Hypothesis 1d (friends), and Hypothesis 1e (possessions).

Identification with continuers.

Participants responded to six statements about their perceived state after the incident. Two questions probed their identification with person A and B, respectively. The responses to these two questions offer an alternative route to analyzing the influence of the location of the five features.

We calculated two ANOVAs (see Table B and Table C in S1 Supporting Information), with the five between-subjects factors and the two statements describing identification with person A or person B as the respective criterion (as identification—unlike monetary allocation—did not have a fixed-sum constraint, the second ANOVA is not redundant). In both ANOVAs, we observed a significant main effect of psychology (F(1, 660) = 70.26, p < .001, partial η² = .10 for person A and F(1, 662) = 44.83, p < .001, partial η² = .06 for person B) and memory (F(1, 660) = 76.50, p < .001, partial η² = .10 and F(1, 662) = 59.32, p < .001, partial η² = .08). In both ANOVAs, parameter signs indicated that the person with each respective component received more money. The only other significant effect was a weak three-way interaction between body, friends, and possessions (F(1, 662) = 8.69, p = .003, partial η² = .01) for person B. This result is difficult to interpret and may be due to sampling error (the corresponding effect for person A was virtually nonexistent (F(1, 660) = .15, p = .70, partial η² = .00). The pattern of results is thus very similar to the one obtained for monetary allocations; in other words, the data support Hypothesis 2 (participants’ personal reidentification with either continuer followed the same pattern across conditions as the monetary allocation).

Explicit weighting of dimensions.

Fig 3 summarizes participants’ answers to the 10 questions assessing how they perceived each of the five dimensions to be related to identity and survival, respectively.

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Fig 3. Importance assigned to the five dimensions for identity and survival (N = 704).

Triangles denote the means and blue bars show the histogram for answers to the five identity questions; dots and orange bars show the corresponding information for the survival questions. Whiskers signify the 99% confidence intervals for the means.

https://doi.org/10.1371/journal.pone.0228271.g003

The five dimensions were gauged to be of similar importance for identity and survival; in addition, answers pertaining to the same dimension were highly correlated (the full intercorrelation matrix is included Table E in S1 Supporting Information). Friends were judged to be slightly more important for identity than for survival, on average. Corresponding to the main effect of the ANOVA reported above, psychology and memory were considered more important than the other three dimensions, again supporting Hypothesis 1b (psychology) and Hypothesis 1c (memory), and given the similar pattern to the ANOVA results, supporting Hypothesis 3 (participants’ subjectively assessed importance of dimensions corresponded to the importance of factors for the allocation decision). In contrast to the previous analysis, body and friends were judged to be of medium to low importance, while only possessions were regarded as unimportant. A closer analysis of the distribution of responses shows that responses for both body and friends spanned the full range of values and were roughly symmetric around the mean. As participants did not make a substantial difference between identity and survival, we can give an affirmative answer to Research Question 1: The importance assigned to each of the five dimensions was similar for identity and survival. In S1 Supporting Information, we explore the connection between the dimensions’ judged importance and their monetary evaluation (see sections 2.1.7. and 2.1.8.).

Given the complete individual explicit ratings of all five conditions, we also searched for subgroups of participants with divergent weighting patterns. We conducted a cluster analysis on the matrix of 10 weightings for all participants (see section 2.1.9. in S1 Supporting Information). The resulting final six cluster centers demonstrate unanimity in the highest ranking of psychology and memory. Only in one cluster were possessions rated somewhat important (along with all other dimensions). The clusters were equally split into considering body relatively important and relatively unimportant, and divided similarly for friends, with two clusters regarding both to be important. These results could be considered as qualified evidence for Hypotheses 1a (body) and 1d (friends), but, again, there is little evidence for Hypothesis 1e (possessions).

Personal reidentification after fission.

The qualitative answers of 521 participants (74%) could be interpreted as reasonable reactions to the encountered scenario; other answers show some sources of confusion or alternative interpretations. For the largest subgroup of 87 participants, their allocation was targeted at mitigating losses, which runs counter to the instructions. The overall pattern indicates a positive answer to Research Question 2: Participants explain their monetary allocation often in reference to closeness or identity relations with continuers. Some of the reasoning involves a direct comparison between continuers, declaring one closer, closest or having “more” of the original person. Participants who allocate close to equal splits claim to be indifferent between continuers, or describe them as deserving equal compensation or payments. Some invoke fairness towards both continuers, which could either be consistent with the closest-continuer theory in that participants see both continuers as other people or indicate an influence of other-regarding preferences not considered in the theory. A complete analysis of participants’ qualitative answers is given in S1 Supporting Information (section 2.3.).

Fig 4 summarizes the responses to the six post-questionnaire items. As the characteristics of person A and person B changed between experimental conditions, we show the maximum and minimum value for each participant (in six cases, one answer was missing; we considered the remaining answer as both minimum and maximum). Participants who identified with one continuer should express a high degree of identification with one person and a low degree of identification with the other. A high minimum indicates a high degree of identification with both continuers; a low maximum, a low degree of identification with both.

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Fig 4. Histogram and means of responses to post-questionnaire items.

Blue bars indicate a tendency to agree with the statement; red bars, to disagree. For the two questions regarding being person A or person B (whose composition differs between conditions), the smaller and the larger value for each participant were pooled and analyzed as minimum and maximum value. Dots represent means; whiskers denote 99% confidence intervals around the means.

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An analysis of all six response distributions revealed that, on average, none of the statements was strongly endorsed or strongly rejected. Participants tended to affirm that they had survived the incident, and identified to some degree with one (but not the other) of the resulting persons. This maximum identification was positively correlated with the maximum percentage of dimensions retained in one of the two persons (r = .103, N = 696, p = .007) and the maximum of the two monetary amounts allocated (r = .265, N = 696, p < .001). On average, participants tended to reject the statement that they were the same person before and after the incident.

Statements suggesting nonexistence or being two persons after the incident were both rejected on average, but the mean response was closer to a position of indifference. On average, participants agreed less with the statement that they were two persons after the accident when memory and psychology were united in one person. An ANOVA with identification with both continuers as criterion showed a significant interaction between the location of memory and psychology (F(1, 663) = 28.43, p < .001, partial η² = .04, see Table D and Fig H in S1 Supporting Information). All averages were close to indifference in all conditions. As the histogram in Fig 4 reveals, this average indifference hides polarized answers, with some participants agreeing strongly and more participants disagreeing strongly.

The monetary allocations also revealed differences between conditions in which memory and psychology components were united versus those in which they were split, as Fig 5 illustrates: When memory and psychology were united, the differences in allocations were larger; when they were split, the differences were smaller (more than 50% of participants split the money roughly equally in this condition).

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Fig 5. Relative frequency of absolute allocation differences, separately for conditions in which memory and psychology were split vs. united (intervals include the upper limit).

https://doi.org/10.1371/journal.pone.0228271.g005

Research Questions 3 and 4 aim at judgments violating transitivity by either identifying with both continuers (Research Question 3) or neither continuer (Research Question 4). There was mixed support for the idea that people violate transitivity in their judgments of identity in either fashion. The S1 Supporting Information (see sections 2.1.1., 2.1.4.–2.1.6.) offers further insight into how the location of psychology and memory influenced participants’ identification with either continuer. The aggregate level results followed the pattern of the ANOVA findings: Identification (and allocation) was higher when memory or psychology continued, particularly when the continuity of both was preserved. Nevertheless, the individual analysis shows some participants identifying with both continuers at the same time and other participants identifying with neither. A second cluster analysis (see section 2.1.10. in S1 Supporting Information) revealed clusters of participants corresponding in their responses to those expected in the relevant three cases in Nozick’s decision scheme (there are always two possible continuers, so Case 1 cannot occur). We found clusters that endorse being two people, being nonexistent, and also being both nonexistent and two people after fission. Cluster membership is significantly related to features of the scenario and monetary splits. Most responses can be interpreted meaningfully through the lens of the closest continuer theory, but we observe interindividual variability and potentially divergent concepts of persons.

Experimental setting and sample.

Participants were again recruited via Amazon Mechanical Turk. The experiment was paired with a second, unrelated economic experiment in a Human Intelligence Task (HIT) lasting an expected 8–12 minutes, with a guaranteed payment of $1 and a possible bonus contingent on responses in the second task. The HIT was restricted to U.S. participants with matching browser location information and self-description and an approval rating of 95% or higher. Double participation was prevented using both the Unique Turker service and an analysis of IP addresses: In cases of multiple participation from one address, the first response was included if there was no temporal overlap with further attempts, resulting in a sample of N = 821 participants who were included in the analysis. One cluster of five suspicious responses was removed on the basis of near-identical IP addresses, identical browser signature, and near-identical comments. The mean age was 33.1 years (SD = 10.0 years) and 52.3% of participants were female.

The study was approved by the ethics committee of the MPI for Human Development in Berlin. Participants gave electronic consent after reading a consent form prior to beginning the study. The study was coded and conducted with Qualtrics, using JavaScript injection and including the libraries jQuery, jQuery UI, and Bootstrap to generate stimuli and tables.

Experimental design.

Study 2 also featured a fictional accident with a transporter pod (see section 1.2 in S1 Supporting Information for a full account). The description of the incident was nearly identical to the one in Study 1, with the same complete 2 × 2 × 2 × 2 × 2 between-subjects factorial design, but the order of features was randomly determined for each participant and the resulting distribution tables were created at run-time in the browser (see Fig 2).

Instead of being asked to determine insurance payments, participants in Study 2 were informed that “’both persons will be compensated for the incident” and asked to make a decision about an inheritance payment:

At the same time, the travel agency informs you that a distant relative of yours has died and that you have been chosen as the sole heir of the relative’s estate. The inheritance cannot be split up into smaller parts and it cannot be sold or divided by other means.

Due to the circumstances of the incident, you are asked to decide which of the persons leaving the pod at your destination should be declared heir, person A or person B (it has to be either A or B; the other person cannot receive any part of the inheritance at any point in time).

Participants were prompted to choose one of the two continuers. Rips and colleagues [17] argued that a closest continuer model should be able to predict the uncertainty associated with choosing, similar to models in decision theory based on weighted dimensions. The experienced uncertainty should be negatively correlated with the distance of continuers on the closeness metric. On a subsequent page, participants were therefore prompted to indicate the difficulty of this decision on a scale from 0 to 10.

Following this, participants responded to a series of statements regarding identity and survival after the hypothesized accident on a continuous slider scale (from “strongly disagree” to “strongly agree”). They also judged the importance of the five dimensions for survival and the importance of 14 partially novel dimensions for identity on a similar continuous scale (from “not at all important” to “extremely important”). The order of survival and identity questions was cross-balanced across participants.

Each participant answered the identity questions for each of the eight singular subdimensions in the five dimensions—body, appearance, psychology, personality, memory, knowledge, friends, and possessions—as well as for a random selection of six of 16 further dimensions, cross-balanced across participants. These 16 dimensions comprised five concerning relationships with others (family, loved ones, colleagues, general relationships with other people, and group membership), four concerning morality and values (moral values, virtues and vices, philosophy of life, religion), three concerning roles and profession (private roles, professional roles, and profession/job), two concerning demographics (gender and nationality), and two summary dimensions: mind and brain. These additional dimensions were chosen to explore to which degree the original dimensions might have led to an over- or underestimation of importance, e.g. if friends might be considered less relevant for personal continuity than close relatives.

Finally, each participant answered a series of questions measuring the tendency to reduce psychological to physical phenomena (see section 1.2.7. in S1 Supporting Information).

Inheritance decision and difficulty ratings.

First, the binary decision between heirs was regressed onto the five factors constituted by the continuity or lack of continuity of the five dimensions. Table 1 shows the results of a binary logistic regression with the criterion “choice of person B” and each feature coded as 1 if present in person B and as 0 if present in person A (and therefore not in person B). Results showed a very strong effect of memory, a strong effect of psychology, weaker effects of body, and friends, but no significant effect of possessions. Fig 6 relates participants’ choices to the location of memory and psychology for different splits of the attributes between the two continuers: The main effects of memory and psychology on inheritance choice do not seem to be dependent on the distribution of other features.

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Table 1. Choice of person B in Study 2: Binary logistic regression, N = 821.

https://doi.org/10.1371/journal.pone.0228271.t001

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Fig 6. Relative frequency (in percent) of choosing person B as heir.

Separate graphs summarize scenarios in which person B retains between one (20%) and four (80%) of the original dimensions. In each graph, allocations are shown for each possible division of the memory and psychology dimension. Note that B cannot retain both dimensions in the 20% condition and A cannot retain both dimensions in the 80% condition. Whiskers show the 99% confidence intervals around the means.

https://doi.org/10.1371/journal.pone.0228271.g006

Combining the binary measure with the difficulty rating allowed us to compute an ANOVA comparable to the one in Study 1: A decision for person B was coded as 1, a decision for person A as –1, then multiplied by the inverse difficulty rating. The combined criterion has a middle point of zero, indicating maximum difficulty for either decision, a minimum value of –10 (decision for A with minimum difficulty) and a maximum value of 10 (decision for B with minimum difficulty). The results of a five-factorial ANOVA using the transformed values as criterion were comparable to those of the logistic regression: We found strong main effects of memory (F(1, 789) = 295.38, p < .001, partial η² = .27) and psychology (F(1, 789) = 97.07, p < .001, partial η² = .11), weaker main effects of body (F(1, 789) = 11.99, p < .001, partial η² = .02) and friends (F(1, 789) = 7.63, p = .006, partial η² = .01), and no main effect of possessions (F(1, 789) = 1.62, p = .20, partial η² = .00). There were no significant interactions (see Table I in S1 Supporting Information).

The inheritance decision data thus again provide strong support for Hypothesis 1b (psychology) and Hypothesis 1c (memory). There is weaker support for Hypothesis 1a (body) and Hypothesis 1d (friends) and no support for Hypothesis 1e (possessions). Shifting the focus to which combination of factors makes decisions more difficult, we ran a second ANOVA with decision difficulty as criterion (see Table J in S1 Supporting Information). The only substantial effect was an interaction between location of memory and psychology (F(1, 789) = 56.31, p < .001, partial η² = .07; see also section 2.2.2. in S1 Supporting Information), followed by a weaker interaction between location of body and memory (F(1, 789) = 6.9, p = .009, partial η² = .01).

Identification with continuers.

Parallel to the analysis conducted in Study 1, we calculated two ANOVAs with the five location variables as factors and the two statements describing identification with person A or person B as criterion (see Table K and Table L in S1 Supporting Information). The strongest effect in both ANOVAs was again the main effect of memory (F(1, 789) = 133.13, p < .001, partial η² = .14 for person A and F(1, 789) = 125.57, p < .001, partial η² = .14 for person B), followed by the main effect of psychology (F(1, 789) = 78.89, p < .001, partial η² = .09 and F(1, 789) = 69.81, p < .001, partial η² = .08). In addition, a significant, but weaker, main effect emerged for friends in both ANOVAs (F(1, 789) = 4.07, p = .04, partial η² = .01 and F(1, 789) = 4.23, p = .04, partial η² = .01), and a significant main effect emerged for body for person A only (F(1, 789) = 5.76, p = .03, partial η² = .01 and F(1, 789) = 3.54, p = .06, partial η² = .00). No interaction effect was consistently significant for both ANOVAs: There was one significant two-factorial and one three-factorial interaction for each. In summary, these results mirror the results of the preceding analysis of the inheritance decision.

Explicit weighting of dimensions.

Fig 7 shows participants’ ratings of the importance of the full set of 24 possible dimensions for determining identity in order of average assigned importance. Together with the pattern of intercorrelations (see Table O and Table P in S1 Supporting Information), this approach allows us to compare the attributes featured in our scenarios with alternatives and to evaluate the relationship between jointly presented features. Memories and personality (here separated from knowledge and psychology) are considered the most important features, closely followed by knowledge and psychology.

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Fig 7. Importance assigned to attributes for determining identity between persons (300 ≤ N ≤ 817) in Study 2.

Dots and bars show means and corresponding 99% CIs. All participants rated the eight dimensions marked with filled dots and a randomly selected subset of six other dimensions (balanced across participants). Elements of the five scenario dimensions are labeled in bold.

https://doi.org/10.1371/journal.pone.0228271.g007

The separate evaluation makes it possible to compare the ratings for otherwise joint dimensions (see section 2.2.3. in S1 Supporting Information): Appearance and body have similar mean ratings and are highly correlated (r = .76, p < .001). Similarly, personality and psychology ratings are correlated (r = .53, p < .001) and, to a lesser degree, memory and knowledge ratings (r = .37, p < .001), and personality and knowledge ratings (r = .37, p < .001). While questions differed from Study 1, we conducted a cluster analysis on the weightings of the eight separate dimensions (see section 2.2.7. in S1 Supporting Information). Most clusters could be replicated in the new cluster analysis. The subdimensions combined in the scenario were rated very similarly in all but one cluster.

Moral values, philosophy of life, and virtues and vices were considered less important than the dimensions described above, but more important than the rest. These findings are inconsistent with previous studies [65] and are considered in more detail in the general discussion. There was a substantial gap between this group of dimensions and religion, indicating that participants did not consider moral values and virtues to be strongly dependent on religion. In addition, ratings for moral values, philosophy of life, and virtues and vices correlated highly with those for personality, psychology, and knowledge and, to a lesser degree, with those for memory and friends, whereas religion ratings were substantially correlated with friends and possessions ratings only.

With respect to attributes describing relationships with other people, family was regarded as most important, followed by relationships with others in general and friends, and—much less important—colleagues. Ratings for family were at least moderately positively correlated with those for all features used in the scenario except psychology and personality. Low importance ratings were given for all attributes relating to profession, as well as for nationality and possessions. In fact, possessions were rated least important, echoing the low importance of this factor in determining decisions in both scenarios.

Participants’ responses to the survival questions were generally in line with those reported in Study 1 with minor deviations. Order effects for survival and identity questions were small and did not come close to change the interpretation of results (see section 2.2.5. in S1 Supporting Information).

Personal reidentification after fission.

Comparing participants’ ratings of the post-questionnaire items between studies (see also section 2.2.4. and Table Q in S1 Supporting Information), the largest differences between the studies were only about half a scale point in size, yet there was a clear pattern to their direction. In Study 2, the maximum identification with one of the two continuers was higher (t(1515) = 7.82, p < .001, two-tailed test), the minimum identification was lower (t(1515) = −4.00, p < .001), endorsements of both personal survival (t(1514) = 6.73, p < .001) and being the same (t(1510) = 4.55, p < .001) were stronger, and there was less agreement with the statement that the original person does not exist after the incident (t(1509) = −3.03, p = .002). There was no significant difference in endorsement of the statement that the original person was now two persons (t(1514) = −1.02, p = .31). This pattern of results is consistent with the idea that the task of splitting money led to a decrease in identification with one continuer (and not the other), but it does not completely explain the phenomenon of intransitivity: Most participants responded with an average minimum score >1 to questions regarding identification with continuers and of >2 to the question regarding being two people after the incident. In other words, some participants again committed a violation of transitivity in identifying the original person with more than one continuer. The continuous scale used in Study 1 is not enough to explain this.

Table 2 summarizes means and intercorrelations of the items tapping participants’ perspectives on identity relations after fission. Answers to questions regarding survival and nonexistence were highly negatively correlated (r = −.57, p < .001), and the acceptance of being two people was positively correlated with the minimum identification with either person (r = .35, p < .001).

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Table 2. Correlations, means, and standard deviations of the six post-questionnaire items and decision difficulty scale, Study 2.

https://doi.org/10.1371/journal.pone.0228271.t002

An ANOVA with agreement that the original person was now two persons as the criterion (see Table M in S1 Supporting Information) again showed a significant interaction of memory and psychology (F(1, 789) = 10.48, p = .001, partial η² = .01), but also interactions between memory and friends (F(1, 789) = 15.60, p < .001, partial η² = .02), body and memory (F(1, 789) = 10.00, p = .002, partial η² = .01), psychology and friends (F(1, 789) = 5.38, p = .02, partial η² = .01), and a four-factorial interaction of body, psychology, friends, and possessions (F(1, 789) = 6.07, p = .01, partial η² = .01). An ANOVA with agreement to nonexistence as criterion (see Table N in S1 Supporting Information) similarly shows an interaction of memory and psychology as strongest effect (F(1, 789) = 22.34, p < .001, partial η² = .03).

Inspecting correlations with the difficulty scale gives further insight into these results: Variation in the perceived difficulty of the decision was negatively correlated with endorsement of survival and staying the same after the incident and positively correlated with a higher minimum identification with both, as well as with endorsement of being either both persons or none after the incident (see Table 2). Consistent with the predictions of the closest continuer theory, ratings for identification were positively related to the percentage of traits retained, and for scenarios with 60%:40% splits of dimensions, ratings for survival and for being the same were the lowest and ratings for being two people and for being nonexistent were the highest (see section 2.2.9. in S1 Supporting Information for visualizations and tests).

Given the presentation of the same six questions as in Study 1, we attempted to replicate the cluster analysis conducted before (see section 2.2.8. in S1 Supporting Information). The new cluster analysis shows a reasonable match for all but one original cluster. Again, cluster membership stood in a significant relationship with features of the encountered scenario.