Related papers: Arrow's Impossibility Theorem: Computability in So…
Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose…
It is shown that, since an ultrafilter over an operator-algebraically finite (i.e. isomorphic to the lattice of projectors of a finite Von Neumann algebra) quantum logic is not necessarily principal, Arrow's Impossibility Theorem doesn't…
In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning…
An impossibility theorem demonstrates that a particular problem or set of problems cannot be solved as described in the claim. Such theorems put limits on what is possible to do concerning artificial intelligence, especially the…
Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…
The classic Gibbard-Satterthwaite theorem says that every strategy-proof voting rule with at least three possible candidates must be dictatorial. In \cite{McL11}, McLennan showed that a similar impossibility result holds even if we consider…
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of…
The anthropic principle is an inevitable constraint on the space of possible theories. As such it is central to determining the limits of physics. In particular, we contend that what is ultimately possible in physics is determined by…
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…
We generalize the Arrow's impossibility theorem--a key result in social choice theory--to the setting where the arity $k$ of the relation under consideration is greater than $2$. Some special but natural properties of $k$-ary relations are…
Utility functions or their equivalents (value functions, objective functions, loss functions, reward functions, preference orderings) are a central tool in most current machine learning systems. These mechanisms for defining goals and…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
We consider the problem of aggregating votes cast by a society on a fixed set of issues, where each member of the society may vote for one of several positions on each issue, but the combination of votes on the various issues is restricted…
Multiwinner voting rules can be used to select a fixed-size committee from a larger set of candidates. We consider approval-based committee rules, which allow voters to approve or disapprove candidates. In this setting, several voting rules…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
We investigate when non-dictatorial aggregation is possible from an algorithmic perspective, where non-dictatorial aggregation means that the votes cast by the members of a society can be aggregated in such a way that there is no single…
Coalitional manipulation in voting is considered to be any scenario in which a group of voters decide to misrepresent their vote in order to secure an outcome they all prefer to the first outcome of the election when they vote honestly. The…
In party-approval multiwinner elections the goal is to allocate the seats of a fixed-size committee to parties based on the approval ballots of the voters over the parties. In particular, each voter can approve multiple parties and each…
With the increasing pervasive use of machine learning in social and economic settings, there has been an interest in the notion of machine bias in the AI community. Models trained on historic data reflect biases that exist in society and…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…