Sequencing Chess

We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude that the state space consists of several pockets between which transitions are rare. Skilled players explore an even smaller subset of positions that populate some of these pockets only very sparsely. These results suggest that the usual measures to estimate both, the size of the state space and the size of the tree of legal moves, are not unique indicators of the complexity of the game, but that topological considerations are equally important

Computing Elo Ratings of Move Patterns in the Game of Go

Move patterns are an essential method to incorporate domain knowledge into Go-playing programs. This paper presents a new Bayesian technique for supervised learning of such patterns from game records, based on a generalization of Elo ratings. Each sample move in the training data is considered as a victory of a team of pattern features. Elo ratings of individual pattern features are computed from these victories, and can be used in previously unseen positions to compute a probability distribution over legal moves. In this approach, several pattern features may be combined, without an exponential cost in the number of features. Despite a very small number of training games (652), this algorithm outperforms most previous pattern-learning algorithms, both in terms of mean log-evidence (−2.69), and prediction rate (34.9%). A 19x19 Monte-Carlo program improved with these patterns reached the level of the strongest classical programs

Optimal Sludge? The Price of Program Integrity

Public officials often impose eligibility requirements for government programs that have two effects: (1) They screen out ineligible people and (2) they screen out eligible people. Consisting of paperwork requirements, interviews, waiting periods, and administrative burdens, such requirements are sometimes characterized as “sludge,” and for some eligible people, they might prove overwhelming or prohibitive. In these circumstances, there is a pervasive normative issue: What is the optimal tradeoff between the screening out of ineligible people and the screening out of eligible people? It is plausible to think that a great deal depends on numbers. If, for example, the number of ineligible people who are screened out is very large, and if the number of eligible people who are screened out is very small, then there would seem little ground for objection. But if the number of eligible people who are screened out is very large, there is a serious problem, and it might be worthwhile to consider an approach that would not screen out eligible people, even if it would simultaneously fail to screen out, or effectively “screen in,” a small number of ineligible people. We identify competing, plausible positions on the normative question, which we label consequentialist (in the sense that they attempt an assessment of the consequences of alternatives approaches, with a focus on numbers) and legalist (in the sense that they emphasize legal constraints, designed to ensure that benefits go only to those who are actually eligible). We also offer the results of a pilot study, which shows that the overwhelming majority of respondents would favor changes that allow ineligible people to receive benefits, if that is the price of ensuring that eligible people do so as well—unless the number of ineligible recipients is very high. The survey results suggest that most people reject the legalist position and embrace a form of consequentialism. We suggest that in light of the normative analysis and the survey results, a form of consequentialism is best, unless the law explicitly forbids it

Rex E. Lee Conference on the Office of the Solicitor General of the United States: Panel for Former Solicitors General

I agree entirely that the chain of command is clear and that the Framers managed to make it all the way through all the articles of the Constitution without even conceiving of a solicitor general, let alone bothering to mention an attorney general. It is important nonetheless to distinguish between those things the solicitor general does pursuant to the longstanding notice-and-comment regulation, and the other things a solicitor general may do pursuant to his (and, someday, her!) statutory obligation to be of general assistance to the attorney general