Nonanonymity and sensitivity of computable simple games

This paper investigates algorithmic computability of simple games (voting games). It shows that (i) games with a finite carrier are computable, (ii) computable games have both finite winning coalitions and cofinite losing coalitions, and (iii) computable games violate any conceivable notion of anonymity, including finite anonymity and measurebased anonymity. The paper argues that computable games are excluded from the intuitive class of gniceh infinite games, employing the notion of ginsensitivityh\-equal treatment of any two coalitions that differ only on a finite set.Voting games, infinitely many players, ultrafilters, recursion theory, Turing computability, finite carriers, finite winning coalitions, algorithms

Arrow's Theorem, countably many agents, and more visible invisible dictators

For infinite societies, Fishburn (1970), Kirman and Sondermann (1972), and Armstrong (1980) gave a nonconstructive proof of the existence of a social welfare function satisfying Arrowfs conditions (Unanimity, Independence, and Nondictatorship). This paper improves on their results by (i) giving a concrete example of such a function, and (ii) showing how to compute, from a description of a profile on a pair of alternatives, which alternative is socially preferred under the function. The introduction of a certain goracleh resolves Miharafs impossibility result (1997) about computability of social welfare functions.Arrow impossibility theorem, Turing computability, recursion theory, oracle algorithms, free ultrafilters

Coalitionally strategyproof functions depend only on the most-preferred alternatives

In a framework allowing infinitely many individuals, I prove that coalitionally strategyproof social choice functions satisfy gtops only.h That is, they depend only on which alternative each individual prefers the most, not on which alternative she prefers the second most, the third, . . . , or the least. The functions are defined on the domain of profiles measurable with respect to a Boolean algebra of coalitions. The unrestricted domain of profiles is an example of such a domain. I also prove an extension theorem.Gibbard-Satterthwaite theorem, dominant strategy implementation, social choice functions, infinitely large societies, tops only

Computability of simple games: A complete investigation of the sixty-four possibilities

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and algorithmic computability. For each such class, we either show that it is empty or give an example of a game belonging to it. We observe that if a type contains an infinite game, then it contains both computable ones and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms.Comment: 25 page

Affidavit of CDAT Counsel

A sworn affidavit of Counsel in Support of Coeur d\u27Alene Tribe\u27s Responsive Briefing and exhibits 1-13 in support thereof

A search for cyclotron resonance features with INTEGRAL

We present an INTEGRAL observation of the Cen-Crux region in order to search the electron cyclotron resonance scattering features from the X-ray binary pulsars. During the AO1 200ks observation, we clearly detected 4 bright X-ray binaries, 1 Seyfert Galaxy, and 4 new sources in the field of view. Especially from GX301-2, the cyclotron resonance feature is detected at about 37 keV, and width of 3--4 keV. In addition, the depth of the resonance feature strongly depends on the X-ray luminosity. This is the first detection of luminosity dependence of the resonance depth. The cyclotron resonance feature is marginally detected from 1E1145.1-6141. Cen X-3 was very dim during the observation and poor statistics disable us to detect the resonance features.These are first INTEGRAL results of searching for the cyclotron resonance feature.Comment: 4pages, 8figures, To be published in the Proceedings of the 5th INTEGRAL Workshop: "The INTEGRAL Universe", February 16-20, 2004, Munic

Computability of simple games: A complete investigation of the sixty-four possibilities

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and computability. For each such class, we either show that it is empty or give an example of a game belonging to it. We observe that if a type contains an infinite game, then it contains both computable infinitegames and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms

Preference aggregation theory without acyclicity: The core without majority dissatisfaction

Acyclicity of individual preferences is a minimal assumption in social choice theory. We replace that assumption by the direct assumption that preferences have maximal elements on a fixed agenda. We show that the core of a simple game is nonempty for all profiles of such preferences if and only if the number of alternatives in the agenda is less than the Nakamura number of the game. The same is true if we replace the core by the core without majority dissatisfaction, obtained by deleting from the agenda all the alternatives that are non-maximal for all players in a winning coalition. Unlike the core, the core without majority dissatisfaction depends only on the players' sets of maximal elements and is included in the union of such sets. A result for an extended framework gives another sense in which the core without majority dissatisfaction behaves better than the core.Comment: 27+3 page

Characterizing the Borda ranking rule for a fixed population

A ranking rule (social welfare function) for a fixed population assigns a social preference to each profile of preferences. The rule satisfies "Positional Cancellation" if changes in the relative positions of two alternatives that cancel each other do not alter the social preference between the two. I show that the Borda rule is the only ranking rule that satisfies "Reversal" (a weakening of neutrality), "Positive Responsiveness," and "Pairwise Cancellation.