相关论文: What majority decisions are possible

We consider contests with a large set (continuum) of participants and axiomatize contest success functions that arise when performance is composed of both effort and a random element, and when winners are those whose performance exceeds a…

In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with…

Given a sequence of integers $a_j, j\ge 1,$ a multiset is a combinatorial object composed of unordered components, such that there are exactly $a_j$ one-component multisets of size $j.$ When $a_j\asymp j^{r-1} y^j$ for some $r>0$, $y\geq…

In this article, we describe an algorithm to determine whether a permutation class C given by a finite basis B of excluded patterns contains a finite number of simple permutations. This is a continuation of the work initiated in [Brignall,…

It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…

We conjecture that if a system S \subseteq {x_i=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}} has only finitely many solutions in integers x_1,...,x_n, then each such solution (x_1,...,x_n) satisfies |x_1|,...,|x_n| \leq…

Recursive permutations whose cycles are the classes of a decidable equivalence relation are studied; the set of these permutations is called $\mathrm{Perm}$, the group of all recursive permutations $\mathcal{G}$. Multiple equivalent…

We consider the following decision problem DMAX#SAT, and generalizations thereof: given a quantifier-free propositional formula $F(\mathbf{x},\mathbf{y})$, where $\mathbf{x},\mathbf{y}$ are tuples of variables, and a bound $B$, determine if…

Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…

In the theory of voting, the Plurality rule for preferences that come in the form of linear orders selects the alternatives most frequently appearing in the first position of those orders, while the Anti-Plurality rule selects the…

Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein's Galois…

We study the functional equation $A\circ X=X\circ B$, where $A,$ $B$, and $X$ are polynomials over $\mathbb C$. Using previous results of the author about polynomials sharing preimages of compact sets, we show that for given $B$ its…

Two-stage superposition choice procedures, which sequentially apply two choice procedures so that the result of the first choice procedure is the input for the second choice procedure, are studied. We define which of them satisfy given…

We present an alternative voting system that aims at bridging the gap between proportional representative systems and majoritarian, single winner election systems. The system lets people vote for multiple parties, but then assigns each…

We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…

Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…

A group $G$ is said to be totally $2$-closed if in each of its faithful permutation representations, say on a set $\Omega$, $G$ is the largest subgroup of $\mathrm{Sym}(\Omega)$ which leaves invariant each of the $G$-orbits for the induced…

A group of individuals wishes to classify $m$ objects into $n$ categories in such a way that no class is left empty, a condition known as surjectivity. The opinions of the individuals are aggregated separately for each object using an…

Many classical social preference (multiwinner social choice) correspondences are resolute only when two alternatives and an odd number of individuals are considered. Thus, they generally admit several resolute refinements, each of them…

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…