arXiv subjects

Egor Ianovski

Publications and source records attributed to Egor Ianovski.

16 recordsLinked to original sources

arXiv2023

Computing the proportional veto core

In social choice there often arises a conflict between the majority principle (the search for a candidate that is as good as possible for as many voters as possible), and the protection of minority rights (choosing a candidate that is not overly bad for particular individuals or groups). In a context where the latter is our main concern, veto-based rules -- giving individuals or groups the ability to strike off certain candidates from the list -- are a natural and effective way of ensuring that no minority is left with an outcome they find untenable. However, such rules often fail to be anonymous, or impose specific restrictions on the number of voters and candidates. These issues can be addressed by considering the proportional veto core -- the solution to a cooperative game where every coalition is given the power to veto a number of candidates proportional to its size. However, the naïve algorithm for the veto core is exponential, and the only known rule for selecting from the core, with an arbitrary number of voters, fails anonymity. In this paper we present a polynomial time algorithm for computing the core, study its expected size, and present an anonymous rule for selecting a candidate from it. We study the properties of core-consistent voting rules. Finally, we show that a pessimist can manipulate the core in polynomial time, while an optimist cannot manipulate it at all.

cs.GT↗

arXiv2022

Welfare effects of strategic voting under scoring rules

Strategic voting, or manipulation, is the process by which a voter misrepresents his preferences in an attempt to elect an outcome that he considers preferable to the outcome under sincere voting. It is generally agreed that manipulation is a negative feature of elections, and much effort has been spent on gauging the vulnerability of voting rules to manipulation. However, the question of why manipulation is actually bad is less commonly asked. One way to measure the effect of manipulation on an outcome is by comparing a numeric measure of social welfare under sincere behaviour to that in the presence of a manipulator. In this paper we conduct numeric experiments to assess the effects of manipulation on social welfare under scoring rules. We find that manipulation is usually negative, and in most cases the optimum rule with a manipulator is different to the one with sincere voters.

cs.GT↗

arXiv2022

How should we score athletes and candidates: geometric scoring rules

Scoring rules are widely used to rank athletes in sports and candidates in elections. Each position in each individual ranking is worth a certain number of points; the total sum of points determines the aggregate ranking. The question is how to choose a scoring rule for a specific application. First, we derive a one-parameter family with geometric scores which satisfies two principles of independence: once an extremely strong or weak candidate is removed, the aggregate ranking ought to remain intact. This family includes Borda count, generalised plurality (medal count), and generalised antiplurality (threshold rule) as edge cases, and we find which additional axioms characterise these rules. Second, we introduce a one-parameter family with optimal scores: the athletes should be ranked according to their expected overall quality. Finally, using historical data from biathlon, golf, and athletics we demonstrate how the geometric and optimal scores can simplify the selection of suitable scoring rules, show that these scores closely resemble the actual scores used by the organisers, and provide an explanation for empirical phenomena observed in biathlon and golf tournaments. We see that geometric scores approximate the optimal scores well in events where the distribution of athletes' performances is roughly uniform.

cs.GT↗

arXiv2022

Comparing the Manipulability of Approval Voting and Borda

The Gibbard-Satterthwaite theorem established that no non-trivial voting rule is strategy-proof, but that does not mean that all voting rules are equally susceptible to strategic manipulation. Over the past fifty years numerous approaches have been proposed to compare the manipulability of voting rules in terms of the probability of manipulation, the domains on which manipulation is possible, the complexity of finding such a manipulation, and others. In the closely related field of matching, Pathak and Sonmez pioneered a notion of manipulability based on case-by-case comparison of manipulable profiles. The advantage of this approach is that it is independent of the underlying statistical culture or the computational power of the agents, and it has proven fruitful in the matching literature. In this paper, we extend the notion of Pathak and Sonmez to voting, studying the families of $k$-approval and truncated Borda scoring rules. We find that, with one exception, the notion does not allow for a meaningful ordering of the manipulability of these rules.

cs.GT↗

arXiv2021

Detecting corruption in single-bidder auctions via positive-unlabelled learning

In research and policy-making guidelines, the single-bidder rate is a commonly used proxy of corruption in public procurement used but ipso facto this is not evidence of a corrupt auction, but an uncompetitive auction. And while an uncompetitive auction could arise due to a corrupt procurer attempting to conceal the transaction, but it could also be a result of geographic isolation, monopolist presence, or other structural factors. In this paper we use positive-unlabelled classification to attempt to separate public procurement auctions in the Russian Federation into auctions that are probably fair, and those that are suspicious.

cs.LG↗

arXiv2020

Electing a committee with dominance constraints

We consider the problem of electing a committee of $k$ candidates, subject to some constraints as to what this committee is supposed to look like. In our framework, the candidates are given labels as an abstraction of a politician's religion, a film's genre, a song's language, or other attribute, and the election outcome is constrained by interval constraints -- of the form "Between 3 and 5 candidates with label X" -- and dominance constraints -- "At least as many candidates with label X as with label Y". The problem is, what shall we do if the committee selected by a given voting rule fails these constraints? In this paper we argue how the logic underlying weakly-separable and best-$k$ rules can be extended into an ordering of committees, and study the question of how to select the best valid committee with respect to this order. The problem is NP-hard, but we show the existence of a polynomial time solution in the case of tree-like constraints, and a fixed-parameter tractable algorithm for the general case.

cs.GT↗

arXiv2017

Complexity of mixed equilibria in Boolean games

Boolean games are a succinct representation of strategic games wherein a player seeks to satisfy a formula of propositional logic by selecting a truth assignment to a set of propositional variables under his control. The framework has proven popular within the multiagent community, however, almost invariably, the work to date has been restricted to the case of pure strategies. Such a focus is highly restrictive as the notion of randomised play is fundamental to the theory of strategic games -- even very simple games can fail to have pure-strategy equilibria, but every finite game has at least one equilibrium in mixed strategies. To address this, the present work focuses on the complexity of algorithmic problems dealing with mixed strategies in Boolean games. The main result is that the problem of determining whether a two-player game has an equilibrium satisfying a given payoff constraint is NEXP-complete. Based on this result, we then demonstrate that a number of other decision problems, such as the uniqueness of an equilibrium or the satisfaction of a given formula in equilibrium, are either NEXP or coNEXP-complete. The proof techniques developed in the course of this are then used to show that the problem of deciding whether a given profile is in equilibrium is coNP^#P-hard, and the problem of deciding whether a Boolean game has a rational-valued equilibrium is NEXP-hard, and whether a two-player Boolean game has an irrational-valued equilibrium is NEXP-complete. Finally, we show that determining whether the value of a two-player zero-sum game exceeds a given threshold is EXP-complete.

cs.GT↗

arXiv2016

Two statements of the Duggan-Schwartz theorem

The Duggan-Schwartz theorem (Duggan and Schwartz, 1992) is a famous result concerning strategy-proof social choice correspondences, often stated as "A social choice correspondence that can be manipulated by neither an optimist nor a pessimist has a weak dictator". However, this formulation is actually due to Taylor (2002), and the original theorem, at face value, looks rather different. In this note we show that the two are in fact equivalent.

cs.GT↗

arXiv2016

Manipulability of consular election rules

The Gibbard-Satterthwaite theorem is a cornerstone of social choice theory, stating that an onto social choice function cannot be both strategy-proof and non-dictatorial if the number of alternatives is at least three. The Duggan-Schwartz theorem proves an analogue in the case of set-valued elections: if the function is onto with respect to singletons, and can be manipulated by neither an optimist nor a pessimist, it must have a weak dictator. However, the assumption that the function is onto with respect to singletons makes the Duggan-Schwartz theorem inapplicable to elections which necessarily select a committee with multiple members. In this paper we make a start on this problem by considering elections which elect a committee of size two (such as the consulship of ancient Rome). We establish that if such a consular election rule cannot be expressed as the union of two disjoint social choice functions, then strategy-proofness implies the existence of a dictator. Although we suspect that a similar result holds for larger sized committees, there appear to be many obstacles to proving it, which we discuss in detail.

cs.GT↗

arXiv2014

DValue for Boolean games is EXP-complete

We show that the following problem is EXP-complete: given a rational v and a two player, zero-sum Boolean game G determine whether the value of G is at least v. The proof is via a translation of the proof of the same result for Boolean circuit games in Feigenbaum et al. (1995).

cs.GT↗

arXiv2014

The existential fragment of S1S over element and successor is the co-Buchi languages

Buchi's theorem, in establishing the equivalence between languages definable in S1S over element and < and the omega-regular languages also demonstrated that S1S over element and < is no more expressive than its existential fragment. It is also easy to see that S1S over element and < is equi-expressive with S1S over element and successor. However, it is not immediately obvious whether it is possible to adapt Buchi's argument to establish equivalence between expressivity in S1S over element and successor and its existential fragment. In this paper we show that it is not: the existential fragment of S1S over element and successor is strictly less expressive, and is in fact equivalent to the co-Buchi languages.

cs.FL↗

arXiv2013

EGuaranteeNash for Boolean Games is NEXP-Hard

Boolean games are an expressive and natural formalism through which to investigate problems of strategic interaction in multiagent systems. Although they have been widely studied, almost all previous work on Nash equilibria in Boolean games has focused on the restricted setting of pure strategies. This is a shortcoming as finite games are guaranteed to have at least one equilibrium in mixed strategies, but many simple games fail to have pure strategy equilibria at all. We address this by showing that a natural decision problem about mixed equilibria: determining whether a Boolean game has a mixed strategy equilibrium that guarantees every player a given payoff, is NEXP-hard. Accordingly, the $ε$ variety of the problem is NEXP-complete. The proof can be adapted to show coNEXP-hardness of a similar question: whether all Nash equilibria of a Boolean game guarantee every player at least the given payoff.

cs.GT↗

arXiv2013

Complexity of equivalence relations and preorders from computability theory

We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relations $R, S$, a componentwise reducibility is defined by $ R\le S \iff \ex f \, \forall x, y \, [xRy \lra f(x) Sf(y)]. $ Here $f$ is taken from a suitable class of effective functions. For us the relations will be on natural numbers, and $f$ must be computable. We show that there is a $Π_1$-complete equivalence relation, but no $Πk$-complete for $k \ge 2$. We show that $Σk$ preorders arising naturally in the above-mentioned areas are $Σk$-complete. This includes polynomial time $m$-reducibility on exponential time sets, which is $Σ2$, almost inclusion on r.e.\ sets, which is $Σ3$, and Turing reducibility on r.e.\ sets, which is $Σ4$.

math.LO↗

arXiv2013

Computable Component-wise Reducibility

We consider equivalence relations and preorders complete for various levels of the arithmetical hierarchy under computable, component-wise reducibility. We show that implication in first order logic is a complete preorder for $\SI 1$, the $\le^P_m$ relation on EXPTIME sets for $\SI 2$ and the embeddability of computable subgroups of $(\QQ,+)$ for $\SI 3$. In all cases, the symmetric fragment of the preorder is complete for equivalence relations on the same level. We present a characterisation of $\PI 1$ equivalence relations which allows us to establish that equality of polynomial time functions and inclusion of polynomial time sets are complete for $\PI 1$ equivalence relations and preorders respectively. We also show that this is the limit of the enquiry: for $n\geq 2$ there are no $\PI n$ nor $\DE n$-complete equivalence relations.

cs.FL↗

arXiv2012

Grammar Logics in Nested Sequent Calculus: Proof Theory and Decision Procedures

A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal operator [a] comes with a converse. Extending previous works on nested sequent systems for tense logics, we show all grammar logics (with or without converse) can be formalised in nested sequent calculi, where the axioms are internalised in the calculi as structural rules. Syntactic cut-elimination for these calculi is proved using a procedure similar to that for display logics. If the grammar is context-free, then one can get rid of all structural rules, in favor of deep inference and additional propagation rules. We give a novel semi-decision procedure for context-free grammar logics, using nested sequent calculus with deep inference, and show that, in the case where the given context-free grammar is regular, this procedure terminates. Unlike all other existing decision procedures for regular grammar logics in the literature, our procedure does not assume that a finite state automaton encoding the axioms is given.

cs.LO↗

arXiv2012

Cake Cutting Mechanisms

We examine the history of cake cutting mechanisms and discuss the efficiency of their allocations. In the case of piecewise uniform preferences, we define a game that in the presence of strategic agents has equilibria that are not dominated by the allocations of any mechanism. We identify that the equilibria of this game coincide with the allocations of an existing cake cutting mechanism.

cs.GT↗