Related papers: On the Arrow property
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…
We investigate semiconjugate rational functions, that is rational functions $A,$ $B$ related by the functional equation $A\circ X=X\circ B$, where $X$ is a rational function of degree at least two. We show that if $A$ and $B$ is a pair of…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
The Expansion property considered by researchers in Social Choice is shown to correspond to a logical property of nonmonotonic consequence relations that is the {\em pure}, i.e., not involving connectives, version of a previously known weak…
The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…
We prove a common generalization of two results, one on rainbow fractional matchings and one on rainbow sets in the intersection of two matroids: Given $d = r \lceil k \rceil - r + 1$ functions of size (=sum of values) $k$ that are all…
When formalized, some diagonal arguments do not show the diagonal object to be impossible but rather reveal some other anomaly (e.g., that one of the relevant sets is ill-defined). This raises the possibility that some diagonal arguments…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
Social Choice theory generalizes voting on one proposal to ranking multiple proposals. Yet, while a vote on a single proposal has the status quo (Reality) as a default, Reality has been forsaken during this generalization. Here, we propose…
Coalition Logic is primarily concerned with what coalitions can achieve, whereas what coalitions cannot achieve -- their \emph{inability} -- has received comparatively little explicit attention. This asymmetry matters in artificial…
A theorem of alternatives provides a reduction of validity in a substructural logic to validity in its multiplicative fragment. Notable examples include a theorem of Arnon Avron that reduces the validity of a disjunction of multiplicative…
It is argued that it is possible to give operational meaning to free will and the process of making a choice without employing metaphysics.
In this paper we are concerned with a Gordan-type theorem involving an arbitrary number of inequality functions. We not only state its validity under a weak convexity assumption on the functions, but also show it is an optimal result. We…
This paper studies the axiomatic bargaining problem and proposes a new class of bargaining solutions, called coarse Nash solutions. These solutions assign to each problem a set of outcomes coarser than that chosen by the classical Nash…
Let $k$ be an algebraically closed field of characteristic zero and $P(x,y)\in k[x,y]$ be a polynomial which depends on all its variables. $P$ has an algebraic constraint if the set $\{(P(a,b),(P(a',b'),P(a',b),P(a,b')\,|\,a,a',b,b'\in k\}$…
This study considers the method to derive a ranking of alternatives by aggregating the rankings submitted by several individuals who may not evaluate all of them. The collection of subsets of alternatives that individuals (can) evaluate is…
Let U be an open subset of a unirational variety (or more generally of a separably rationally connected variety). We prove that there is rational curve C in U such that the fundamental group of C surjects onto the fundamental group of U.…
Path independence is arguably one of the most important choice rule properties in economic theory. We show that a choice rule is path independent if and only if it is rationalizable by a utility function satisfying ordinal concavity, a…