nach oben

Social Choice and Welfare

Erschienen in:

05.09.2016 | Original Paper

Non-bossiness

verfasst von: William Thomson

Erschienen in: Social Choice and Welfare | Ausgabe 3/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

An allocation rule is “non-bossy” if whenever a change in an agent’s preferences does not bring about a change in his assignment, then it does not bring about a change in anybody’s assignment. We discuss the multiple interpretations that have been proposed for this property. We question their validity, arguing that in most cases, non-bossiness either says too little or that it says too much. We also make a case against the property. We propose as its main justification the technical help that it often provides in structuring classes of rules, making characterizations more manageable.

Vorheriger Artikel Efficiency and strategy-proofness in object assignment problems with multi-demand preferences

Nächster Artikel Campaign rhetoric and the hide-and-seek game

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

Serizawa (1999) writes: “It has also been an important research question whether or not we can substitute for nonbossiness a simple, weak, and economically meaningful condition”.

In the language of Thomson (2016), non-bossiness is a “post-application invariance property” of a rule: it states the invariance of certain components of the choice the rule makes with respect to certain changes in the arguments that are subject to conditions whose verification requires that it be applied first.

The index i is generally understood to refer to a specific agent but if (i) is adopted, it may more generally refer to a “position” in an economy. The position may be filled by agents with one of several preferences.

Under the name of “weak non-bossiness (in terms of welfare)”.

These authors use the name of “non-bossiness” and so do Berga and Moreno (2009). Mizukami and Wakayama (2007) and Nishizaki (2012) refer to it as “strong non-bossiness”.

Ritz refer to it as “non-corruptibility”, as he has in mind a strategic interpretation of the property. We prefer avoiding this term because of the other, non-strategic, interpretations that can be given to the property. Berga and Moreno (2009) use the expression “weak non-bossiness”.

Non-bossiness in welfare on both sides is discussed by Mutuswami (1997, 2005) under the name of “strong utility nonbossiness”, and Bade (2015) under the name of “utility non-bossiness”. Both authors provide examples of rules revealing, in the context of two different types of allocation problems, the absence of a direct logical relation between non-bossiness and non-bossiness in welfare on both sides.

These authors refer to it as “weak non-bossiness”, Mizukami and Wakayama (2007), as “quasi-strong non-bossiness”, and Berga and Moreno (2009) as “quasi-non-bossiness”.

These authors propose the group-restricted version under the name of “H-respectfulness”, H designating the pre-specified group. It is for an easier comparison with the other properties that we present two versions of it. Raghavan (2014a) discusses a property that is closely related to the unlimited version. Raghavan (2014b) discusses another conditional invariance property that is logically independent of non-bossiness.

Nath and Sen (2014) refer to it as “allocation non-bossiness”.

Saijo et al. (2007) refer to the first property as “the outcome rectangular property” and to the second one as “the rectangular property”. Mizukami and Wakayama (2005) formulate the requirement, under the name of “the weak rectangular property”, that under the same hypotheses as the rectangle property, both agents find the new outcome at most as desirable as the initial outcome according to their initial preferences.

Of course, if it is manipulable, it may well be manipulable by more than one agent, and to really understand the consequences of the behavior, we should engage in its full-fledged game-theoretic analysis. For each preference profile, we should identify the equilibria of the manipulation game associated with it, and compare the resulting allocation(s) to the allocation that would have been selected in the absence of manipulation (Hurwicz 1972).

Olson (1991) and Miyagawa (1997) have proposed that the two properties be merged. The first author refers to a rule satisfying their conjunction as “non-strategic” and the second as “strongly strategy-proof”.

To the best of our knowledge, this is the first paper in which an implication of this type has been established.

This interpretation is proposed by Ritz (1983).

The property is usually called “Maskin monotonicity”.

The property is introduced by Moulin (1987) in the context of binary social choice under the name of “agreement”. It has been studied in a wide variety of models. For another application, see Thomson (1993), For a survey, see Thomson (1999).

For a dictatorial rule, there is an agent, chosen ahead of time and once and for all, whose welfare the rule always maximizes. The same alternatives may all be most preferred for several of his possible preferences, and among them, the rule may select in a manner that leaves his assignment unchanged but makes the other agents’ assignments depend on what his preferences are. Given an order on the agent set, the sequential priority rule associated with that order selects the alternative that is most preferred by the agent who is first if there is a unique such alternative; if not, among the alternatives that are most preferred by this agent, it selects the one that is most preferred by the agent who is second, if there is a unique such alternative, and so on. Non-bossiness holds because the order is specified before preferences are known.

We say “typically” because a “conditional” type of sequential priority rule can be defined for which at each step, the identity of the agent who is next is made to depend on the preferences of the agents who have chosen so far. Such a rule is obviously bossy.

Adachi and Kongo (2013) propose a version of non-bossiness in welfare on both sides, under the name of “strong non-bossiness in welfare”, which has an even closer connection to welfare-dominance under preference-replacement. On the hypothesis side, indifference is required for only one of the relations that are contemplated for the agent whose preferences change, and the requirement is that all other agents find their assignments when he makes that particular announcement at least as desirable as when he makes the second announcement. The two preference relations that are contemplated for agent i do not play the same role, so the requirement is not that the welfare of all of the other agents be unchanged. The hypotheses are weaker than those of welfare-dominance.

The consistency “principle” has been the object of a large literature, reviewed in Thomson (2015a). The axiom of consistency can also be written for solution correspondences, but since here we focus on its connection to non-bossiness, a property of rules, we have stated it for rules.

In fact, consistency implies the strong form of a “separability” property, which itself implies a group version of non-bossiness (Sect. 7.1).

This is the case whenever the reduction operation is “transitive”. This means that reducing an economy with agent set N with respect to some subgroup \(N'\) of N and some outcome x, and then reducing the resulting economy with respect to some subgroup \(N''\) of \(N'\) and \(x_{N'}\), is the same thing as directly reducing the initial economy with respect to \(N''\) and x. Transitivity holds for the models discussed in these pages.

Balinski and Young (1982) restate consistency as the requirement that “Every part of a fair allocation should be fair”.

Of course, non-bossiness does not imply consistency. To see this, it suffices to consider, in our variable-population framework, a sequential priority rule in which the orders in which assignments are calculated are chosen independently population by population. For consistency, the orders with which the components of a sequential priority rule are associated should be induced from a single reference order on the entire population of potential agents.

In the context of object allocation problems, random priority rules have the same feature of achieving some sort of fairness across economies (in the expected sense) but not in each economy separately (in the ex post sense). However, because each agent still has to be assigned an object, the extent to which some agents are favored by a sequential priority rule is significantly less than what is the case for the dictatorial rules that we have discussed.

There are plenty of similar situations. In bargaining theory, continuity of a rule is very compelling, and not imposing continuity is not the same thing as endorsing any kind of discontinuous behavior. We cannot go into details here, but the tradeoffs between continuity, Pareto-optimality, and monotonicity are well-known.

This discussion is based on Thomson (2015b).

There are domains on which the Walrasian correspondence is single-valued and non-bossy. An example is the domain of Cobb-Douglas economies. The Walrasian definition can also be applied to object-reallocation problems when each agent owns one object and consumes at most one (Shapley and Scarf 1974). It is equivalent on this domain to Gale’s “top-trading-cycle rule”, which is non-bossy.

Under the names of “coalitional nonbossiness”, “strong nonbossiness”, and “group non-bossiness”.

Afacan (2012) provides an example in the context of object allocation problems to make the point.

Under the name of “total non-bossiness”.

One definition is proposed by Bogomolnaia et al. (2005).

An example of such a characterization is based on the individual-endowments lower bound, anonymity in welfare, and strategy-proofness (Ashlagi and Serizawa 2012). Related results are due to Saitoh and Serizawa (2007), Sakai (2008, (2013), and Chew and Serizawa (2007).

This is an object-allocation problem in which each object comes with a priority relation over its possible recipients.

This rule is commonly known as the “deferred acceptance mechanism”.

This rule is commonly known as the “Boston mechanism”.

In the context of several-to-one two-sided matching, no selection from the stable correspondence is non-bossy (Kojima 2010). In fact, non-bossiness is incompatible with weaker requirements than stability (Kongo 2013). Thus, we can deduce from these results the non-existence of selections from the stable correspondence, or rules satisfying these weaker requirements, as well as each of the properties that we have enumerated imply non-bossiness.

The argument applies even if preferences are not required to be strictly convex. If linear preferences were in the domain, it would suffice to give agent i preferences whose level curves are hyperplanes normal to the prices p.

Abdulkadiroğlu A, Sönmez T (2003) School choice: a mechanism design approach. Am Econ Rev 93:729–747CrossRef

Adachi T, Kongo T (2013) First-price auctions on general preference domains: axiomatic characterizations. Econ Theory Bull 1:93–103CrossRef

Afacan M (2012) On the “group non-bossiness” property. Econ Bull 32:1571–1575

Alcalde J (1996) Implementation of stable solutions to marriage problems. J Econ Theory 69:240–254CrossRef

Alcalde-Unzu J, Molis E (2011) Exchange of indivisible goods and indifferences: the top trading absorbing sets mechanisms. Games Econ Behav 73:1–16CrossRef

Ashlagi I, Serizawa S (2012) Characterizing Vickrey allocation rule by anonymity. Soc Choice Welf 38:531–542CrossRef

Atlamaz M, Yengin D (2008) Fair Groves mechanisms. Soc Choice Welf 31:573–587CrossRef

Bade S (2015) Multilateral matching under dichotomous preferences. Mimeo

Balinski M, Young P (1982) Fair Representation. Yale University Press, New Haven

Barberà S, Berga D, Moreno B (2010) Individual versus group strategy-proofness: when do they coincide? J Econ Theory 145:1648–1674CrossRef

Barberà S, Berga D, Moreno B (2016) Group strategy-proofness in private good economies. Am Econ Rev 106:1073–1099CrossRef

Barberà S, Jackson M (1995) Strategy-proof exchange. Econometrica 63:51–87CrossRef

Barberà S, Jackson M, Neme A (1997) Strategy-proof allotment rules. Games Econ Behav 18:1–21CrossRef

Berga D, Moreno B (2009) Strategic requirements with indifference: single-peaked versus single-plateaued preferences. Soc Choice Welf 32:275–298CrossRef

Bogomolnaia A, Deb R, Ehlers L (2005) Incentive-compatibility on the full preference domain. J Econ Theory 123:161–185CrossRef

Chew SH, Serizawa S (2007) Characterizing the Vickey combinatorial auction by induction. Econ Theor 33:393–406CrossRef

Chun Y (1999) Equivalence of axioms for bankruptcy problems. Int J Game Theory 28:511–520CrossRef

Chun Y (2006) The separability principle in economies with single-peaked preferences. Soc Choice Welf 26:239–253CrossRef

Doğan B (2016) Nash-implementation of the no-envy solution on symmetric domain of economies. Games Econ Behav 98:165–171CrossRef

Doğan B, Klaus B (2016) Object allocation via immediate-acceptance: characterizations and an affirmative action application. Mimeo

Dur U (2015) The modified Boston mechanism. Mimeo

Ehlers L (2014) Top trading with fixed tie-breaking in markets with indivisible goods. J Econ Theory 151:64–87CrossRef

Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7:45–98

Gale D, Shapley L (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15CrossRef

Gibbard A (1973) Manipulation of voting schemes. Econometrica 41:587–601CrossRef

Harless P (2016) Immediate acceptance with or without skips: comparing school assignment procedures. Mimeo

Hashimoto K, Saitoh H (2012) Strategy-proof cost sharing under increasing returns: improvement of the supremal welfare loss. Mimeo

Hurwicz L (1972) On informationally decentralized systems. In: McGuire CB, Radner R (eds) Chapter 14 in Decision and Organisation. University of Minnesota Press, Minneapolis, pp 297–336

Jaramillo P, Manjunath V (2012) The difference indifference makes in strategy-proof allocation of objects. J Econ Theory 147:1913–1946CrossRef

Ju B-G (2013) Coalitional manipulation on networks. J Econ Theory 148:627–662CrossRef

Klaus B (2001a) Population-monotonicity and separability for economies with single-dipped preferences and the assignment of an indivisible object. Econ Theor 17:675–692CrossRef

Klaus B (2001b) Coalitional strategy-proofness in economies with single-peaked preferences and the assignment of an indivisible object. Games Econ Behav 34:64–82CrossRef

Klaus B, Bochet O (2013) The relation between monotonicity and strategy-proofness. Soc Choice Welf 40:41–63CrossRef

Kojima F (2010) Impossibility of stable and nonbossy matching mechanisms. Econ Lett 107:69–70CrossRef

Kongo T (2013) On non-bossy matching rules in two-sided matching problems. Int J Econ Theory 9:303–311CrossRef

Le Breton M, Zaporozhets V (2009) On the equivalence of coalitional and individual strategy-proofness properties. Soc Choice Welf 33:287–309CrossRef

Long Y (2016) Strategy-proof group selection under single-peaked preferences over group size. Mimeo

Manjunath V (2012) When too little is as good as nothing at all: rationing a disposable good among satiable people with acceptable thresholds. Games Econ Behav 74:576–587CrossRef

Manjunath V (2014) Efficient and strategy-proof social choice when preferences are single-dipped. Int J Game Theory 43:579–597CrossRef

Maskin E (1999) Nash equilibrium and welfare optimality. Rev Econ Stud 66:83–114 (first circulated in 1977)CrossRef

Mishra D, Quadir A (2014) Non-bossy single object auctions. Econ Theory Bull 2:93–110CrossRef

Miyagawa E (1997) Strategy-proofness for the reallocation of multiple indivisible goods. University of Rochester, Mimeo

Mizukami H, Wakayama T (2007) Dominant strategy implementation in economic environments. Games Econ Behav 60:307–325CrossRef

Mizukami H, Wakayama T (2009) The relation between non-bossiness and monotonicity. Math Soc Sci 58:256–264CrossRef

Morimoto S, Serizawa S (2015) Strategy-proofness and efficiency with nonquasi-linear preferences: a characterization of minimum price Walrasian rule. Theor Econ 10:445–487CrossRef

Morimoto S, Serizawa S, Ching S (2013) A characterization of the uniform rule with several commodities and agents. Soc Choice Welf 40:871–911CrossRef

Moulin H (1987) The pure compensation problem: egalitarianism versus laissez-fairism. Q J Econ 101:769–783CrossRef

Mukherjee C (2015) On axioms underlying the use of reserve price. Mimeo

Mutuswami S (1997) Strategyproof and coalitionally strategyproof mechanisms for cost sharing

Mutuswami S (2005) Strategyproofness, non-bossiness, and group strategy-proofness in a cost sharing model. Econ Lett 89:83–88CrossRef

Nagahisa N (1991) A local independence condition for characterization of Walrasian allocations rule. J Econ Theory 54:106–123CrossRef

Nagahisa R, Suh S-C (1995) A characterization of the Walras rule. Soc Choice Welf 12:335–352CrossRef

Nash JF (1950) The bargaining problem. Econometrica 18:155–162CrossRef

Nath S, Sen A (2015) Affine maximizers in domains with selfish valuations. ACM Trans Econ Comput 3(26):1–19CrossRef

O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2:345–371CrossRef

Olson M (1991) Dominant and Nash strategy mechanisms for the assignment problem. Mimeo

Pápai S (2000a) Strategy-proof assignment by hierarchical exchange. Econometrica 68:1403–1433CrossRef

Pápai S (2000b) Strategyproof multiple assignment using quotas. Rev Econ Design 5:91–105CrossRef

Pápai S (2001b) Strategyproof and nonbossy multiple assignments. J Public Econ Theory 3:257–271CrossRef

Pápai S (2003) Strategyproof exchange of indivisible goods. J Math Econ 39:931–959CrossRef

Pazner E, Schmeidler D (1978) Egalitarian equivalent allocations: a new concept of economic equity. Q J Econ 92:671–687CrossRef

Raghavan M (2014a) Sufficient conditions for weak group strategy-proofness. Mimeo

Raghavan M (2014b) Efficient pairwise allocation with priority trading. Mimeo

Rhee S (2011) Strategy-proof allocation of indivisible goods among couples. Jpn Econ Rev 62:289–303CrossRef

Ritz Z (1983) Restricted domains, Arrow social welfare functions and noncorruptible and non-manipulable social choice correspondences: the case of private alternatives. Math Soc Sci 4:155–179CrossRef

Saijo T, Sjöström T, Yamato T (2007) Secure implementation. Theor Econ 2:203–229

Saitoh H, Serizawa S (2007) Vickrey allocation rule with income effect. Econ Theor 35:391–401CrossRef

Sakai T (2008) Second price auctions on general preference domains: two characterizations. Econ Theor 37:347–356CrossRef

Sakai T (2013) An equity characterization of second price auctions when preferences may not be quasi-linear. Rev Econ Design 17(1):17–26CrossRef

Sakai T, Wakayama T (2011) Uniform, equal division, and other envy-free rules between the two

Satterthwaite M (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorem for voting procedures and social choice functions. J Econ Theory 10:187–217CrossRef

Satterthwaite M, Sonnenschein H (1981) Strategy-proof allocation mechanisms at differentiable points. Rev Econ Stud 48:587–597CrossRef

Schummer J (2000) Manipulation through bribes. J Econ Theory 91:180–198CrossRef

Serizawa S (1999) Strategy-proof and symmetric social choice functions for public good economies. Econometrica 67:121–145CrossRef

Shapley L, Scarf H (1974) On cores and indivisibility. J Math Econ 1:23–28CrossRef

Shenker S (1992) Some technical results on continuity, strategy-proofness, and related strategic concepts. Mimeo

Sönmez T, Switzer T (2013) Matching with (branch-of-choice) contracts at United States military academy. Econometrica 81:451–488CrossRef

Thomson W (1987) The vulnerability to manipulative behavior of economic mechanisms designed to select equitable and efficient outcomes. In: Groves T, Radner R, Reiter S (eds) Chapter 14 of Information, Incentives and Economic Mechanisms. University of Minnesota Press, USA, pp 375–396

Thomson W (1993) The replacement principle in public good economies with single-peaked preferences. Econ Lett 42:31–36CrossRef

Thomson W (1999) Welfare-domination under preference-replacement: a survey and open questions. Soc Choice Welf 16:373–394CrossRef

Thomson W (2005) Divide-and-permute. Games Econ Behav 52:186–200CrossRef

Thomson W (2011) Fair allocation rules. In: Arrow K, Sen A, Suzumura K (eds) Handbook of Social Choice and Welfare. North-Holland, Amsterdam, New York, pp 393–506CrossRef

Thomson W (2012) On the axiomatics of resource allocation: Interpreting the consistency principle. Econ Philos 28:385–421CrossRef

Thomson W (2015a) Consistent allocation rules. Mimeo

Thomson W (2015b) Strategy-proof allocation rules. Lecture notes

Thomson W (2016) Designing allocation rules. Mimeo

Wakayama T (2016) Bribe-proofness for single-peaked preferences: characterizations and maximality-of-domains results. Mimeo

Yengin D (2012) Egalitarian-equivalent Groves mechanisms in the allocation of heterogenous objects. Soc Choice Welf 38:137–160CrossRef

Yengin D (2013a) Identical preferences lower bound for allocation of heterogeneous tasks and NIMBY problems. J Public Econ Theory 15:580–601CrossRef

Yengin D (2013b) Population monotonic and strategy-proof mechanisms respecting lower bounds. J Math Econ 49:389–397CrossRef

Titel: Non-bossiness
verfasst von: William Thomson
Publikationsdatum: 05.09.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 3/2016
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-016-0987-7

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 3/2016

Accounting for the spouse when measuring inequality of opportunity

Characterizations of the cumulative offer process

Proportional Borda allocations

A characterization of the Gini segregation index

Rationalizability of Plott consistent choice functions: a corrigendum

On the uniqueness of the yolk

Premium Partner