# Workshop programme

Wednesday, September 27, 2017

9.30-10.00 Brief Introduction and Opening/Welcome

10.00-13.00 Session 1 (11.00-11.30 Coffee Break)

Professor Mehmet Remzi Sanver (Istanbul Bilgi University, Murat Sertel Center for Advanced Economic Studies, Istanbul, Turkey)

Positively responsive collective choice rules and majority rule: a generalization of May’s theorem to many alternatives

Authors: Martin J. Osborne and M. RemziSanver

A collective choice rule selects a set of alternatives for each collective choice problem. Suppose that the alternative x is in the set selected by a collective choice rule for some collective choice problem. Now suppose that x rises above another selected alternative y in some individual’s preferences. If the collective choice rule is “positively responsive”, x remains selected but y is no longer selected. If the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule (May 1952). If the set of alternatives contains three or more members, a large set of collective choice rules satisfy these three conditions. We show, however, that in this case only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash’s version of “independence of irrelevant alternatives” for the domain of problems that have strict Condorcet winners. Further, no rule satisfies the four conditions for the domain of all preference relations.

Professor Andrey Subochev (National Research University Higher School of Economics, Moscow, Russia)

Axiomatic analysis of the union of minimal externally stable sets concerning application and implementation of this novel social choice correspondence

A set of related majority rule-based social choice correspondences are considered: the union of minimal Р-dominating sets D (Duggan 2011, Subochev 2017) the union of weakly stable sets WS(Aleskerov&Kurbanov 1999), the union of minimal P-externally stable sets PES (Wuffl et al. 1989, Subochev 2008) and the union of minimal R-externally stable sets RES (Aleskerov&Subochev 2009, 2013). It has been found that PES and RES both satisfy the following axioms: monotonicity with respect to changes in social preferences (P-monotonicity), the generalized Nash independence of irrelevant alternatives, the idempotence, the Aizerman-Aleskerovproperty, the independence of social preferences for irrelevant alternatives (the independence of losers), but they do not satisfy the extension axiom (Sen’s property ). It has also been demonstrated that MPD satisfies neither of these axioms, and MWS satisfies P-monotonicity only. It has been also found that PES and RES both satisfy the Sanver monotonicity (Özkal-Sanver&Sanver, 2010). Thus, despite they are not Maskin monotonic, these social choice correspondences can be implemented in a nonstandard setting, where actors have (extended) preferences for sets of alternatives. It has also been demonstrated that D and WS do not satisfy Sanver monotonicity.

Professor Vincent Merlin (The University of Caen, Caen, Normandy, France)

Evaluating the likelihood of the referendum paradox for mixed voting systems

Authors: Vincent Merlin, Michel Le Breton and Dominique Lepelley

A referendum paradox (Nurmi, 1999) occurs, in a two party competition, each time a party gets a majority of the seats in the parliament while it did not obtain a majority of votes nationwide. The election of George W. Bush in 2000 (with 271 electoral vote against 267, but less votes than Albert Gore) can be viewed as an occurrence of the paradox. In fact, any two tiers voting systems can be plagued by this flaw. This paradox can be also viewed as an instance of the Borda paradox, as the voting rules fails to select the Condorcet winner. Feix, Lepelley, Merlin and Rouet (2004), Wilson MC, G Pritchard (2007) andLepelley, Merlin and Rouet (2011) computed the probability of the referendum paradox under the IC and IAC assumptions when two parties compete in A equal sized districts. A priori models for voting are extensively described in Gerhlein (2006).

The same paradox may occur for mixed electoral systems. On the top of electing A representatives in districts, the voters also elect D members of the parliament at large. Hence, the parliament is of size A+D. Blais and Massicote (2009) propose an extensive survey of all the mixed electoral systems that are used worldwide. In this paper, assuming that A representative are elected in equal size jurisdictions, we estimate the probability of the referendum paradox for different mixed systems : 1) when the D at large seats are apportioned according to the proportional rule and 2) when the all the D at large seats are attributed to the party which obtained a majority of votes nationwide.

Professor Alexander Karpov (National Research University Higher School of Economics, Moscow, Russia)

Preference diversity orderings

Applying new preference diversity axiomatics, a generalization of the Alcalde-Unzu and Vorsatz (SocChoiceWelf 41(4):965–988, 2013) criterion is developed.

It is shown that all previously used indices violate this criterion. Two new indices (geometric mean-based and leximax-based) that satisfy a new criterion are developed. Leximax-based orders act as a polarization index and are compared to the polarization index of Can et al. (Math Soc Sci 78:76–79, 2015). New impossibility results are obtained.

13.00-14.30 Lunch

14.30-17.30 Session 2

Professor Daniel Karabekyan (National Research University Higher School of Economics, Moscow, Russia)

Manipulability of generalized scoring rules

In this paper we consider 3 alternative and class of scoring rules, where each alternative have a score of (1, a, 0) depending on its place in individual preferences. We consider 4 types of rules: scoring rules (alternatives with the highest sum of scores wins) and 3 types of scoring elimination rules: when we eliminate alternative with the lowest score, alternatives with score lower than average or not higher than average. We find out that the least manipulable depends on the extension axiom or tie-breaking rule. In most cases best results are for parameter "a" not equal to 0,5 or 0, but very close to it. Another result is that scoring elimination rules are less manipulable than scoring rules almost for all "a".

Mrs. Yulia Veselova (National Research University Higher School of Economics, Moscow, Russia)

Individual Manipulation under Incomplete Information

We consider the problem of manipulation in an election by a single voter under incomplete information, i.e., voters know the result of an opinion poll (the outcome of a poll information function, e.g., a list of scores or a set of winners). In this case, a voter has an incentive to misrepresent his preferences if he knows that he will not become worse off and there is a chance of becoming better off. We consider six social choice rules and eight types of poll information functions differing in their informativeness.To compare manipulability, first we calculate the probability that there is a voter that has an incentive to manipulate and show that this measure is not illustrative in the case of incomplete information. Then we suggest considering two other measures: the probability of a successful manipulation and an aggregate stimulus of voters to manipulate, both of which demonstrate more intuitive behavior. We provide results of simulations as well as analytical proofs of some effects observed.

Professor Jean-Francois Laslier (Paris School of Economics, Paris, France)

Voting, Politics, and Football

The Vote Foot Project conducted a survey where 4000 respondents voted for the best football player of the year under three different electoral systems. We find that the voting system is not decisive, that is, Messi is the winner under each system. Furthermore, there is no evidence of strategic voting. We also find surprising connections between political attitudes and opinions about football.

Professor AlainTrannoy (Aix-Marseille School of Economics, Aix-Marseille University, France)

A game framework to understand the outbreak of WW1

We build a decision model enabling to predict the choice between war and peace and we embed it in a game theoretical framework. The decision model articulates root causes as the risk of future war and other contingent factors such as the potential gains/losses in case of victory/defeat and the potential losses linked to the war itself. We calibrate the model to the case of British, French, German and Russian decision-makers at the end of July 14. The timing of decisions of Entente’s partners, who did not coordinate their answers, represents a key factor of the outbreak of war in July 14, with the risk of war which was floating in the air.

Professor Fuad T. Aleskerov (National Research University Higher School of Economics, Moscow, Russia)

Polarization and allocation of migrants

We consider the settlements with initial distribution of population and initial distribution of polarization in these settlements. Then we consider migrants with the distribution of polarization among them. Main assumption is that after allocation of migrants in the settlements the final polarization can be changed, thus, this effect should be taken into account.

Thursday, September 28, 2017

10.00-13.00 Session 3 (11.00-11.30 Coffee Break)

Competitive equilibria in Shapley-Scarf markets with coalitional trade

Authors: Fatma Aslan (Istanbul Bilgi University and Cnam, Paris), Jean Lainé,(Cnam Paris and Murat Sertel Center for Advanced Economic Studies, Istanbul Bilgi University)

We investigate the existence and Core stability properties of several types of competitive equilibria in markets for pure indivisibles where trades are organized between groups of agents. Equilibrium concepts are defined according to the type of cooperation prevailing within coalitions. We show that existence crucially depends on the definition of group budget sets, where individual incomes may or not be merged into group incomes.

Professor Mehmet Barlo (Sabanci University, Istanbul, Turkey)

Ex Post Implementation with Boundedly Rational Agents

Authors: Mehmet Barlo, NuhAygunDalkiran

We provide necessary and sufficient conditions for epsilon - ex post implementation. Our analysis extends Bergemann and Morris (2008) to allow for epsilon - bounded rationality. Yet our necessity condition, epsilon - ex post monotonicity, and Bergemann and Morris's (2008) necessity condition, ex post monotonicity, are not nested. Epsilon - ex post implementation adds another dimension of robustness to ex post implementation in terms of bounded rationality.

Professor Semih Koray (Bilkent University, Ankara, Turkey)

Implementation via rights structures

Authors: SemihKoray, Kemal Yildiz

We introduce a new institutional framework for implementation, which takes the power distribution in the society as its point of departure. The power distribution is formalized by the notion of a rights structure introduced by M. Sertel. We formulate and characterize implementability via rights structures under several different specifications. We also identify how implementation via rights structures is related to implementation via mechanisms. In particular, we find the class of rights structures, implementability via which is equivalent to Nash and strong Nash implementability, respectively, in the presence of at least three agents.

Professor Saptarshi Mukherjee (Indian Institute of Technology, Delhi, India)

Implementation in Undominated Strategies by Bounded Mechanisms

Authors: S. Mukherjee, N. Muto, E. Ramaekers and A. Sen

We consider implementation in undominated strategies by bounded mechanisms. Jackson (1991) provides a necessary condition that any implementable SCC satisfies but leaves the sufficiency as an open question. Borgers (1991) also discusses several open questions related to implementation of efficient compromise alternatives. We provide answers to several such questions.

13.00-14.30 Lunch

14.30-17.00 Session 4

` Professor Vera Danilina (Aix-Marseille University, Marseille, France)

Optimal Information Provision in Environmental Policy Design

Information provision is a relatively recent but steadily growing environmental policy tool that varies in forms and targeted activities. Its efficiency is based on a wide range of factors including policy design, characteristics of the market, and the degree of eco-awareness of all economic agents. Our research provides a framework that allows to build an optimal information provision environmental policy accounting for consumer eco-concerns heterogeneity. We explore four different policy scenarios based on two main criteria: (1) a type of decision-maker - government and/or industry association, (2) regulation compulsion for producers - mandatory (eco-certification) or voluntary (eco-labelling). Our study proposes a clear and simple strategy that can be implemented by policy-makers conditionally on the particular characteristics of the market and regulatory goals.

Professor Ipek Ozkal Sanver (Istanbul Bilgi University, Istanbul, Turkey)

One-Sided Matching Problems with Capacity

Authors: DuyguNizamogullari, IpekOzkal-Sanver

Classical roommate problems define individual rationality by conceiving remaining single as the "outside option". This conception implicitly assumes that there is no capacity constraint, i.e., the number of individuals does not exceed the number of the rooms. However, there are many instances when this is not the case. We introduce roommate problem with capacity constraint where the "outside option" is "having no room". In this general framework with capacity, we show that the core equals the set of matchings which are Pareto optimal and stable.

Professor Ahmet Ugur Alkan (Sabanci University, Istanbul, Turkey)

Matching with Information Acquisition

We consider matching under costly information acquisition (e.g., interviewing) by a stylized one-to-one market where (i) Students’ rankings over Universities are based on perfect information but (ii) Universities’ rankings over Students are based on partial information (e.g., exam score) and improvable by interview. Each University in Stage 1 chooses two students to interview and in Stage 2 submits a ranking to a Center which implements the University optimal stable matching. This game mimics the National Intern Resident Matching Program game. We show that pure strategy Nash equilbria, implying stable interview schedules, may fail to exist. There is a unique pure strategy equilibrium where interviewees hierarchically overlap (forming a “ladder”) if and only if students’ preferences are “effectively homogeneous”.

Professor Emre Dogan (National Research University Higher School of Economics, Moscow, Russia)

Ordinal Efficiency and Implementing Random Assignment by Sequential Object Lotteries

We study the random assignment problem. We provide two new conditions and show that they are equivalent to the well known ordinal efficiency criterion. The equivalence with the first one – sequentially full distribution of objects (SFDO) – suggests that the natural procedure to impelemnt (should be corrected as implement) an ordinally efficient random assignment is by sequential object lotteries rather than the canonical procedure that draws lotteries over deterministic assignments. Moreover, it yields an easy and more importantly very intuitive algorithm to check whether a random assignment is ordinally efficient or not. The equivalence of ordinal efficiency to our second condition – perceived procedural fairness – suggests that for individuals to unanimously percieve (should be corrected as perceive) the impelementation (should be corrected as implementation) of a random assignment by a sequence of object lotteries fair, the random assignment should necessarily be ordinally efficient.

17.00 Closing Remarks