Representation in majority tournaments
نویسندگان
چکیده
The paper presents a general setting for studying majority-based collective decision procedures where the electorate is divided into constituencies according to an equal-representation principle. It generalizes the well-known Referendum Paradox to the non-dichotomous choice case, and shows that all Condorcet choice rules are sensitive to the design of the apportionment of the electorate, in the sense that final outcomes may entirely differ from those prevailing when there is a single constituency. Direct and representative democratic systems thus lead to mutually inconsistent collective decisions. 2000 Elsevier Science B.V. All rights reserved.
منابع مشابه
A Recurrence for Bounds on Dominating Sets in k-Majority Tournaments
A k-majority tournament is realized by 2k−1 linear orders on the set of vertices, where a vertex u dominates v if u precedes v in at least k of the orders. Various properties of such tournaments have been studied, among them the problem of finding the size of a smallest dominating set. It is known that 2-majority tournaments are dominated by 3 vertices and that k-majority tournaments are domina...
متن کاملRealizing Small Tournaments Through Few Permutations
Every tournament on 7 vertices is the majority relation of a 3-permutation profile, and there exist tournaments on 8 vertices that do not have this property. Furthermore every tournament on 8 or 9 vertices is the majority relation of a 5-permutation profile.
متن کاملt-Pancyclic Arcs in Tournaments
Let $T$ be a non-trivial tournament. An arc is emph{$t$-pancyclic} in $T$, if it is contained in a cycle of length $ell$ for every $tleq ell leq |V(T)|$. Let $p^t(T)$ denote the number of $t$-pancyclic arcs in $T$ and $h^t(T)$ the maximum number of $t$-pancyclic arcs contained in the same Hamiltonian cycle of $T$. Moon ({em J. Combin. Inform. System Sci.}, {bf 19} (1994), 207-214) showed that $...
متن کاملEdge-disjoint Hamiltonian Paths and Cycles in Tournaments
We describe sufficient conditions for the existence of Hamiltonian paths in oriented graphs and use these to provide a complete description of the tournaments with no two edge-disjoint Hamiltonian paths. We prove that tournaments with small irregularity have many edge-disjoint Hamiltonian cycles in support of Kelly's conjecture.
متن کاملAcyclic Sets in k-Majority Tournaments
When Π is a set of k linear orders on a ground set X, and k is odd, the k-majority tournament generated by Π has vertex set X and has an edge from u to v if and only if a majority of the orders in Π rank u before v. Let fk(n) be the minimum, over all k-majority tournaments with n vertices, of the maximum order of an induced transitive subtournament. We prove that f3(n) ≥ √ n always and that f3(...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Mathematical Social Sciences
دوره 39 شماره
صفحات -
تاریخ انتشار 2000