Related papers: Majority and Plurality Problems
Using derandomization, we provide an upper bound on the compression size of solutions to the graph coloring problem. In general, if solutions to a combinatorial problem exist with high probability and the probability is simple, then there…
We show that, for a continuous set of entangled four-partite states, the task of maximizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality…
Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…
Several differential equations usually appearing in mathematical physics are solved through a power series expansion, which reduces in solving difference equations. In this paper a probability problem is presented whose solution follows a…
In many institutional settings, $k$ items are selected with the goal of representing the underlying distribution of claims, opinions, or characteristics in a large population. We study environments with two adversarial parties whose…
The topic of diversity is an interesting subject, both as a purely mathematical concept and also for its applications to important real-life situations. Unfortunately, although the meaning of diversity seems intuitively clear, no precise…
How often will elections end in landslides? What is the probability for a head-to-head race? Analyzing ballot results from several large countries rather anomalous and yet unexplained distributions have been observed. We identify tactical…
We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its…
Electing a committee of size k from m alternatives (k < m) is an interesting problem under the multi-winner voting rules. However, very few committee selection rules found in the literature consider the coalitional possibilities among the…
We discuss the minimal number of vertices in a graph with a large chromatic number such that each ball of a fixed radius in it has a small chromatic number. It is shown that for every graph $G$ on $\sim((n+rc)/(c+rc))^{r+1}$ vertices such…
When many labels are possible, choosing a single one can lead to low precision. A common alternative, referred to as top-$K$ classification, is to choose some number $K$ (commonly around 5) and to return the $K$ labels with the highest…
In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the…
Concentration bounds are given for throwing balls into bins independently according to a distribution $p$. The probability of a $k$-loaded bin after $m$ balls is shown to be controlled on both sides by $\rho_{m,k} := m \|p\|_k / k$. This…
A quantitative method is suggested, where meanings of words, and grammatic rules about these, of a vocabulary are represented by real numbers. People meet randomly, and average their vocabularies if they are equal; otherwise they either…
In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…
We study the approximability of Max Ones when the number of variable occurrences is bounded by a constant. For conservative constraint languages (i.e., when the unary relations are included) we give a complete classification when the number…
We generalize Ebert's Hat Problem for three persons and three colors. All players guess simultaneously the color of their own hat observing only the hat colors of the other players. It is also allowed for each player to pass: no color is…
This note characterizes every qualified majority voting rule in environments with just two alternatives through anonymity, responsiveness, and q-neutrality. Crucially, the latter imposes independence of the labels of the alternatives if and…
A majority coloring of a directed graph is a vertex coloring in which each vertex has the same color as at most half of its out-neighbors. In this note we simplify some proof techniques and generalize previously known results on various…
We study a model of a competing population of N adaptive agents, with similar capabilities, repeatedly deciding whether to attend a bar with an arbitrary cutoff L. Decisions are based upon past outcomes. The agents are only told whether the…