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Theory and Decision

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01.01.2015

Collectively ranking candidates via bidding in procedurally fair ways

verfasst von: Werner Güth

Erschienen in: Theory and Decision | Ausgabe 1/2015

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Abstract

Different evaluators typically disagree how to rank different candidates due to their idiosyncratic concerns for the various qualities of the candidates. Our ranking mechanism asks all evaluators to submit individual bids assigning a monetary amount for each possible rank order. The rules specify for all possible vectors of such individual bids the collectively binding rank order of candidates and the payments, due to the different evaluators. Three requirements uniquely determine procedurally fair ranking rules as a game form. Only when additionally assuming exogenously given true evaluations of collective rankings, which may be commonly or only privately known, and—in case of private information—beliefs concerning the evaluations by others, this game form determines proper games and allows for (game theoretic) equilibrium analysis. After an illustration, the approach is adjusted to situations where one wants to rank only acceptable sets of candidates thus rendering the mechanism even more attractive.

Vorheriger Artikel A Bayesian model of Knightian uncertainty

Nächster Artikel A note on equivalent comparisons of information channels

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One could also imagine some TV or radio station financed by contributions of its customers whose program composition is determined by collectively ranking its different components.

For the literature on such more ambitious mechanism design in the sense of (welfare) optimal revelation mechanisms see, for instance, Mas-Colell et al. (1995) and Moulin (1988).

So, for instance, the legal rules for public procurement (e.g., in Germany) require sealed bids and determine the lowest bidder as the contractor with the delivery price equal to his bid (see Güth 2011).

In the example of the lowest bid price procurement auction, there exists an obvious overbidding incentive since a bidder can only gain a positive profit by overbidding his true cost.

According to the revelation principle, one can determine for each equilibrium of each game an allocation equivalent revelation mechanism (general truth telling is an equilibrium but not necessarily in dominant strategies). Thus, one can search for an, e.g., welfare optimal outcome in the class of revelation mechanisms (see Güth forthcoming, for a comparison with legal institutional design).

The bidding mechanism is not restricted to rankings of candidates (for a related study where one bids for public projects, see Güth and Kliemt 2013).

Axiom E guarantees envy-free net exchanges according to bids for all evaluators (such envy-free net exchanges together with Axiom E characterize the first price auction; Güth 2011).

For public provision Güth (2014) allows for subgroups of bidders what excludes outsiders from payment obligations but, due to the outsider problem, questions some of desirable properties of the procedural fairness approach.

Payoffs would have to be interpreted as payoff differences compared to the status quo of no collective ranking.

This is typical for legal institutional design. It only determines the game form via legal or constitutional rules which then, given the specific circumstances of a case, provides the basis for a game theoretic analysis by including the players’—here the evaluators’—true evaluations as well as the beliefs concerning the true evaluations of other evaluators.

By experimentally inducing complete information the study, however, does not demonstrate the main advantage of being applicable also in the realistic case of no well-defined games (Güth et al. (2014) report on experiments illustrating this advantage).

The main advantage of our procedural fairness approach is, however, its applicability irrespective of the common knowledge assumptions of game theoretic equilibrium analysis.

The assumption of \(c_j \left( b \right) =0\) for all \(j\in N\) in the first part of axiom A could be derived from Axiom E\(^\prime \) rather than being imposed.

Condorcet, M. J. Marquis de .(1785). Essai sur l’application de l’analyse à la probabilité des décisions rendues à la plurité des voix. Paris.

Güth, W. (2011). Rules (of bidding) to generate equal stated profits: An axiomatic approach. Journal of Institutional and Theoretical Economics, 167(4), 608–612.

Güth, W. Mechanism design and the law. In F. Parisi (Ed.), Oxford handbook of law and economics. New York: Oxford University Press (forthcoming).

Güth, W. Endogenous community formation and collective provision—A procedurally fair mechanism. Journal of Economic Behavior & Organization (Special issue) 2014.

Güth, W., & Kliemt, H. (2013). Consumer sovereignty goes collective. Ethical basis, axiomatic characterization and experimental evidence. In M. Held, G. Kubon-Gilke, & R. Sturn (Eds.), Normative und institutionelle Grundfragen der Ökonomik. Grenzen der Konsumentensouveränität Jahrbuch 12 (pp. 83–98). Marburg: Metropolis.

Güth, W., & Selten, R. (1991). Majority voting in the Condorcet Paradox as a problem of equilibrium selection, game equilibrium models. In R. Selten (Ed.), Social and political interaction (Vol. IV, pp. 7–40). Berlin: Springer.

Güth, W., Levati, M. V., & Montinari, N. (forthcoming). Ranking alternatives by a fair bidding rule: A theoretical and experimental analysis. European Journal of Political Economy.

Güth, W., Kliemt, H., Koukoumelis, A., Levati, M. V., & Ploner, M. Procedurally fair collective provision: its requirements and experimental functionality. In M. Stadler et al. (Eds.) Proceedings volume, Ottobeuren 2014.

Harsanyi, J. C. (1967/1968). Games of iIncomplete information played by Bayesian players. Management Science, 14, 159–182, 320–334, 486–502.

Mas-Colell, A., Whinston, E., & Green, J. (1995). Microeconomic theory. Oxford: Oxford University Press.

Myerson, R. B. (1979). Incentive compatibility and the bargaining problem. Econometrica, 47(1), 61–74.CrossRef

Moulin, H. (1988). Axioms of cooperative decision making. Cambridge: Cambridge University Press.CrossRef

Titel: Collectively ranking candidates via bidding in procedurally fair ways
verfasst von: Werner Güth
Publikationsdatum: 01.01.2015
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 1/2015
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-013-9412-1

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