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Evaluating opportunities when more is less

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Abstract

There exists psychological evidence that consumers do not consider all available items in the market, which can lead to the “more-is-less” effect, a phenomenon where having more options causes a welfare reduction (Llears et al. in J Econ Theory 170:70–85, 2017). Under this more-is-less effect, we face a dilemma that adding new opportunities may both improve and worsen individual well-being. This study proposes a hypothesis that “more is always better,” which implies that adding new opportunities cannot worsen individual well-being, is a bias to which moral heuristics leads. A satisfactory resolution of this dilemma is act-consequentialism over menus, which is an ex-post and third-party evaluation of opportunity sets. We provide an axiomatic foundation for act-consequentialism over menus and apply it to policymakers’ menu-providing policies.

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Notes

  1. In technical terminology, weak set monotonicity is the principle that if one opportunity set is a subset of another, then the latter must be at least as desirable as the former in terms of individual well-being.

  2. In all fairness, Gaertner (1993), Klemisch-Ahlert (1993), and Puppe (1995, 1996) highlight this issue in the economics literature on freedom and welfare. See also Dworkin (1982).

  3. See Buturak and Evren (2017) and Sarver (2008) for anticipated regret models, where a DM is averse to having more options.

  4. LMNO explain that the competition filter property is satisfied by various decision heuristics, such as Top N (Rubinstein & Salant, 2006), Shortlisting (Manzini & Mariotti, 2007), Categorization (Manzini & Mariotti, 2012), and Rationalization (Cherepanov et al., 2013).

  5. R is a weak order if it is a complete (\(\forall x,y\in X\), xRy or yRx) and transitive (\(\forall x,y,z\in X\), [xRy and yRz] \(\Rightarrow xRz\)) binary relation over X.

  6. In the main body of LMNO’s paper, they consider linear orders, which are complete, transitive, and antisymmetric (\(\forall x,y\in X\), [xRy and yRx] \(\Rightarrow x=y\)) binary relations over X and a choice function that associates a single alternative to each menu. Subsequently, LMNO extend their analysis to the case of weak orders and a choice correspondence in the Appendix.

  7. In the LMNO paper, the condition \(C(T_{i})\cap S_{i}\ne \emptyset\) in the definition of NCCR seems to be lost. The proof of their Theorem 2 would work by adding this condition.

  8. The transitive closure \(R_{C}^{+}\) of \(R_{C}\) is defined as follows: For all \(x,y\in X\), let \(xR_{C}^{+}y\) if there exists a natural number k and \(x_{0},\ldots ,x_{k}\in X\) such that \(x=x_{0}\) and \(x_{i-1}R_{C}x_{i}\) for all \(i=1,\ldots ,k\) and \(x_{k}=y\).

  9. \(R_{C}\) is Suzumura-consistent if for all \(x,y\in X\), \(xR_{C}^{+}y\Rightarrow \lnot [yP_{C}x]\). Suzumura-consistency is weaker than transitivity and is a necessary and sufficient condition to ensure that a binary relation has an ordering extension. See Suzumura (1976) for further details.

  10. In LMNO’s terminology, S is welfare-enhancing over T if \(x\in C(S)\) and \(y\in C(T)\) exist such that \(xR_{C}^{+}y\).

  11. \(\succsim\) is a quasi-order if it is reflexive (\(\forall x\in X\), xRx) and transitive binary relation over \(\mathscr {X}\).

  12. If we require RRP for all \(S, T\in \mathscr {X}\), then the existence of the more-is-less effect represented in Definition 3 implies that WSM is incompatible with that RRP.

  13. The smallest binary relation satisfying a property can be defined as the intersection of binary relations satisfying the property.

  14. A potential issue is whether Sen would consider WSM to be plausible even under our arguments. He may keep defending WSM as a DM should be responsible for the bad consequence of his or her choice (See, for example, Arneson, 1989, 1999). Meanwhile, he may accept only the “intersection” of WSM and RRP as Theorem 2 steps beyond the “intersection” to the “union.” We do not intend to explore the issue any further.

  15. Arrow (1995) states that “I am not an intuitionist in the sense of accepting intuition itself as grounds for moral judgement, but of course, intuitions are evidence of values that can and should be explicitly characterized” (p. 8).

  16. See Jones and Sugden (1982), Nehring and Puppe (1999), and Pattanaik and Xu (1998) for the multiple-preferences approach for evaluating opportunity sets.

  17. Kreps (1979) proposes a similar interpretation that WSM can be seen as a preference for flexibility under uncertainty about future preferences on the set of outcomes.

  18. We consider the argument to be hypothetical because no empirical evidence exists that directly supports it.

  19. Note that it does not mean that the conclusion is logically deduced from the more-is-less effect. Furthermore, it is not equivalent to the argument that WSM is intuitively implausible. Rather, our hypothesis provides a reason why WSM is intuitively plausible but we feel that something is wrong with it.

  20. Reutskaja et al. (2018) suggest that activity in the dorsal striatum and anterior cingulate cortex reflects the value of menus and can serve as a neural indicator of choice overload.

  21. Puppe (1995) states that WSM “seems to be satisfied in any model of ranking sets of alternatives in which the decision maker himself (and not “nature” or an opponent) determines the final outcome. At least, this will be true if one neglects “decision costs”, or other restrictions on the decision maker’s ability to choose from his opportunities” (p. 142).

  22. Baron (1994) suggests that “nonconsequentialist principles arise from overgeneralizing rules that are consistent with consequentialism in a limited set of cases. Commitment to such rules is detached from their original purposes” (p. 1).

  23. For example, Sen (1979) defines act-consequentialism as follows: “An action \(\alpha\) is right if and only if the state of affairs x resulting from \(\alpha\) is at least as good as each of the alternative states of affairs that would have resulted respectively from the alternative feasible acts” (p. 464).

  24. Suzumura and Xu (2001) formalize the intrinsic value of freedom of choice by substantially the same condition as this condition.

  25. A further alternative definition of act-consequentialism over menus may be available. For example, suppose that a DM occupies a responsible position in society and his or her choice influences its members. A question is as follows: How should we evaluate the lists (or menus) of his or her discretionary actions that are restricted by law? If we can obtain any social binary relation over X through a social choice procedure, then it is possible to answer the question by replacing \(R_{C}^{+}\) which defines act-consequentialism over menus with it.

  26. Dworkin (1982) states that “I conclude that neither the instrumental nor noninstrumental value of having choices supports the view that more are always preferable to fewer. In the realm of choice, as in all others, we must conclude–enough is enough” (p. 60).

  27. \(|\cdot |\) denotes the cardinality of a set.

  28. One of the two reviewers suggests this concern.

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Acknowledgements

The author is grateful to the editor of this journal and two anonymous reviewers for their helpful comments and suggestions. This research is supported by a Grant-in-Aid for Scientific Research (C) from the Japan Society for the Promotion of Science (JSPS) (grant number 20K01567). Of course, the remaining errors are the author’s own.

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  1. Faculty of International Politics and Economics, Nishogakusha University, 6-16 Sanbancho, Chiyoda-ku, Tokyo, 102-8336, Japan

    Yukinori Iwata

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Iwata, Y. Evaluating opportunities when more is less. Theory Decis 95, 109–130 (2023). https://doi.org/10.1007/s11238-022-09914-8

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