Morton D. Davis

The 3/2's Rule in Presidential Campaigning

The purpose of this article is to assess the effect of the winner-take-all feature of the Electoral College on the allocation of resources by candidates to the states in a presidential campaign. Conceptualizing the campaign as a two-person zero-sum infinite game, it is found that the main effect of this feature is to induce candidates to allocate campaign resources roughly in proportion to the 3/2s power of the electoral votes of each state, which creates a peculiar bias that makes voters living in the largest states as much as three times as attractive campaign targets as voters living in the smallest states. Empirically, it is shown that the 3/2s rule explains quite well the time allocations of presidential and vice-presidential candidates in the 1960, 1964, 1968, and 1972 campaigns; for presidential campaigns in 1976 and 1980, optimal allocations are indicated for all fifty states and the District of Columbia. A comparison with optimal allocations under a system of direct popular-vote election of the president reveals that such a system would be less susceptible to manipulative strategies than the Electoral College as well as being compatible with the egalitarian principle of “one man, one vote.”

The Geometry of the Arms Race

This article develops a new methodology for analyzing the arms race between the two superpowers based on an extension of the classic Prisoners Dilemma game to allow for sequences of moves. The sequence that is formally analyzed depends on a scenario in which each side: (1) possesses an ability to detect what the other side is doing with a specified probability, and (2) pursues a tit-for-tat policy of conditional cooperation—i.e., cooperates if it detects the other side is cooperating, otherwise does not. Given the detection probabilities and the reciprocity norm, the article demonstrates geometrically, when conditional cooperation between the superpowers is rational and, therefore, likely to occur. It discusses policy implications of this analysis for SALT and advances a qualified suggestion for the sharing of intelligence data. It concludes with suggestions for applying the methodology to other games and multistage game scenarios that mirror the dynamics of plausible sequences of moves.

Optimal Jury Selection: A Game-Theoretic Model for the Exercise of Peremptory Challenges

Potential jurors with a priori probabilities of voting for conviction are assumed to be chosen randomly from a population and to come up one at a time for decision. Defense and prosecution must decide whether to accept or challenge a potential juror as a function of his a priori probability, the distribution of these probabilities in the population, the number of jurors remaining to be selected, and the number of peremptory challenges both sides have remaining. We find a recursive algorithm that minimizes for the defense, and maximizes for the prosecution, the expected probability of conviction in the jury-selection game. A number of conclusions are drawn from numerical calculations of optimal strategies and values in this game, and the analysis is extended to cover the case of peremptory challenges to groups of potential jurors.

Optimal Resource Allocation in Presidential Primaries

Abstract A model for the optimal allocation of resources in presidential primaries is described, under the assumption that two candidates seek to maximize their expected delegate vote in a sequential game that allows for momentum transfer from earlier to later contests. Specifically, the model assumes that the probability that a voter in a primary state votes for a particular candidate is a function of both the resources that candidate and his opponent allocate to that primary and their performances in the immediately preceding primary - and indirectly on all earlier primaries. Given that the candidates make equal (optimal) allocations to each primary, a local maximum, which heavily emphasizes the earlier primaries, is found. Several modifications in the basic model are discussed. Preliminary financial expenditure data are used to test the basic model for the 1976 primaries, and some cursory comparisons with 1980 are made. Possible normative implications of changes in the primary rules are briefly considered, particularly with respect to inequities the present rules seem to engender.

On artificial machine learning: some ideas in search of a theory†

In this paper an algorithm for machine learning is defined and justified heuristically and empirically. “Consistency” properties of perfect evaluation functions are derived and these are used to select the best of a family of evaluation functions, that is, that evaluation function that is most consistent. Methods peculiar to a particular game such as rote learning, looking ahead are generally eschewed; “learning” consists of finding the evaluation which is most consistent. In the game of Nim, in which the winning strategy is well-known, we show that these principles are sufficient to derive a perfect evaluation function (under appropriate conditions) and so arrive at a winning behavioral strategy. In the Mod(6) game, for which a winning strategy is also known, we use the algorithm to deduce an evaluation function and evaluate its effectiveness. Finally, in the game of Hex we match the algorithm with a random player and observe its success.