The voting paradox … with a single voter? Implications for transitivity in choice under risk

Butler, David; Blavatskyy, Pavlo R.

doi:10.1017/s026626711900004x

Cited by 7 publications

(8 citation statements)

References 53 publications

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“…An alternative hypothesis is that the incidence of true intransitive preference cycles might be affected (reduced or increased) with higher stakes. With very high stakes, Butler and Blavatskyy (2020) argue it would be reasonable to select the alternative with the higher probability of the larger prize, even if that strategy induces intransitive choices (see also Fishburn, 1991). To test such rival theories about effects of incentives, one could conduct an experiment with random assignment to incentive conditions and use TE analysis to test among these alternative theories: That incentives influence only error rates, or actually change true preferences.…”

Section: Discussionmentioning

confidence: 99%

Testing transitivity of preference in individuals.

Birnbaum¹

2023

Decision

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This experiment tested transitivity of preferences in individuals using the stimulus design of Butler and Pogrebna (2018). That design was constructed to find violations of transitivity that would occur if people chose the alternative with a higher probability of yielding better outcomes. Each choice problem was presented 60 times (replicated twice in each of 30 sessions). The individual true and error (TE) model was used to estimate incidence of transitive and intransitive preference patterns and error rates for each choice problem for each person. Although the data of most participants were consistent with transitivity, 7 of 22 participants showed significant evidence of intransitive preferences patterns at least part of the time, and 14 participants showed evidence of changing true preferences over time. Systematic violations of the assumption that responses are independently and identically distributed (iid) were observed. Although TE models assume errors are mutually independent, they do not imply that responses will satisfy iid; instead, responses will violate independence when there is a mixture of preference patterns. Markov true and error (MARTER) models in which parameters can change gradually over sessions imply positive correlations between the frequency of preference reversals and the gaps between sessions. Positive correlations were observed for 21 of 22 participants; these were significant for all but 7, 4 of whom were compatible with a single true preference pattern throughout the study. Advantages of TE models (which can analyze response patterns and choice proportions) over older approaches (which analyze only binary choice proportions) are discussed.

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Section: Discussionmentioning

confidence: 99%

Testing transitivity of preference in individuals.

Birnbaum¹

2023

Decision

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“…Many people consider transitivity to be both rational and also descriptive of risky decision making. But there are some who argue that transitivity is neither rational nor descriptive (e.g., Fishburn, 1991;Butler & Blavatskyy, 2020;McNemara, et al, 2014). Butler and Pogrebna (2018) theorized that if a person follows a binary decision rule of choosing the alternative that has a higher probability of yielding a better outcome, then that person would show systematic violations of transitivity of preference in specially constructed choice problems.…”

Section: Introductionmentioning

confidence: 99%

Reanalysis of Butler and Pogrebna (2018) using true and error model

Birnbaum

2020

Judgm. decis. mak.

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Butler and Pogrebna (2018) devised triples of three-branch gambles theorized to violate transitivity of preference according to a most probable winner model. According to this model, a person chooses the option that has the higher probability to yield a better outcome than the other alternative. They tested 11 triples with 100 participants and found cases that appeared to violate weak stochastic transitivity and the triangle inequality. But tests of weak stochastic transitivity and the triangle inequality do not provide a proper method to compare transitive and intransitive models that allow mixtures of preference patterns and random errors. Those older methods can yield false conclusions regarding transitivity, for example, if different participants have different true preferences or if different choice problems have different rates of error. This paper reanalyzes their data using a true and error (TE) model, which does not require these unrealistic assumptions, and which provides estimates of the incidence of transitive and intransitive behavior in a mixture. Reanalysis indicated that 3 of the 11 triples showed convincing evidence of violations of transitivity in the opposite direction of the predictions of the most probable winner model. Further, these and other triples showed other significant violations of the most probable winner model. Despite some violations of the true and error model, the data of Butler and Pogrebna appear to contradict not only transitive utility models but they also refute the most probable winner model as a descriptive theory of choice behavior.

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“…The STP shows how reliance on transitivity over three binary comparisons can lead to a Pareto-inferior choice in the third comparison; is there nothing decision theory can learn from that? As an analogy, observe that the frequency of lottery triples, of the kind studied, meeting the STP is up to 1/56 of all unique triples (Butler & Blavatskyy, 2020). This proportion is a little less than one-third that for the comparable Condorcet 'paradox of voting' cycles, which is 1/18.…”

mentioning

confidence: 83%

“…In Butler and Pogrebna (2018), we tailor made lottery triples to this new recipe and labelled them 'STP triples'. For details of our recipe and the reasoning behind them, see Butler and Pogrebna (2018) and Butler and Blavatskyy (2020).…”

mentioning

confidence: 99%

“…However, the STP shows that we can construct pairs of lotteries for which three binary comparisons should violate transitivity. Assuming that the decision maker's preference is to maximise the probability of earning the greater return, to obey transitivity in these cases would produce a less advantageous outcome (Butler & Blavatskyy, 2020). (In contrast, not obeying transitivity outside the STP structure would result in the less advantageous outcome.)…”

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confidence: 99%

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Intransitive preferences or choice errors? A reply to Birnbaum

Butler

2020

Judgm. decis. mak.

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Birnbaum (2020) reanalyses the data from Butler and Pogrebna (2018) using his ‘true and error’ test of choice patterns. His results generally support the evidence we presented in that paper. Here we reiterate the reasons for our agnosticism as to the direction any cycles might take, even though the paradox that motivated our study takes a ‘probable winner’ direction. We conclude by returning to the potential significance of predictably intransitive preferences for decision theory generally.

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The voting paradox … with a single voter? Implications for transitivity in choice under risk

Cited by 7 publications

References 53 publications

Testing transitivity of preference in individuals.

Testing transitivity of preference in individuals.

Reanalysis of Butler and Pogrebna (2018) using true and error model

Intransitive preferences or choice errors? A reply to Birnbaum

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