Consistent representative democracy

The concept of distance rationalizability has several applications within social choice. In the context of voting, it allows one to define (rationalize) voting rules via a consensus class (roughly, a set of elections in which it is obvious who should win) and a distance function: namely, a candidate is said to be an election winner if it is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be represented in this manner. In this paper, we provide new results on distance rationalizability of several well-known voting rules such as all scoring rules, Approval, Young's rule and Maximin. We also show that a previously published proof of distance rationalizability of Young's rule is incorrect: the consensus notion and the distance function used in that proof give rise to a voting rule that is similar to---but distinct from---the Young's rule. Finally, we demonstrate that some voting rules cannot be rationalized via certain notions of consensus. To the best of our knowledge, these are the first non-distance-rationalizability results for voting rules.

This paper is concerned with the problem of optimizing the performance of a stochastic system over a finite set of alternatives in situations where the performance of the system cannot be evaluated analytically, but must be estimated or measured, for instance, through simulation. We present two variants of a new method for solving such discrete stochastic optimization problems. This new method uses global search to look for the optimal solution. It generates a sequence taking values in the set of feasible alternatives, where each new element of the sequence is generated by comparing the current element with another candidate alternative and letting the next element of the sequence be the one of the current and candidate alternatives that appears to yield better performance. For both versions of the proposed method, the element of the set of feasible alternatives that the generated sequence visits most often is shown to converge almost surely to a globally optimal solution of the underlying optimization pr...

Consider a finite set of alternatives under risk which have multiple attributes. MARPI is an interactive computer-based procedure to find an efficient choice in the sense of linear expected utility. The choice is based on incomplete information about the decision maker's preferences which is elicited and processed in a sequential way. The information includes qualitative properties of the multivariate utility function such as monotonicity, risk aversion, and separability. Further, in case of an additively separable utility function, bounds on the scaling constants are elicited, and preferences (not necessarily indifferences) between sure amounts and lotteries are asked from the decision maker. The lotteries are Bernoulli lotteries generated by MARPI using special strategies. At every stage of the procedure the efficient set of alternatives is determined with respect to the information elicited so far.

Lu and Boutilier proposed a novel approach based on "minimax regret" to use classical score based voting rules in the setting where preferences can be any partial (instead of complete) orders over the set of alternatives. We show here that such an approach is vulnerable to a new kind of manipulation which was not present in the classical (where preferences are complete orders) world of voting. We call this attack "manipulative elicitation." More specifically, it may be possible to (partially) elicit the preferences of the agents in a way that makes some distinguished alternative win the election who may not be a winner if we elicit every preference completely. More alarmingly, we show that the related computational task is polynomial time solvable for a large class of voting rules which includes all scoring rules, maximin, Copeland α for every α ∈ [0,1], simplified Bucklin voting rules, etc. We then show that introducing a parameter per pair of alternatives which specifies the minimum number of partial preferences where this pair of alternatives must be comparable makes the related computational task of manipulative elicitation NP-complete for all common voting rules including a class of scoring rules which includes the plurality, k-approval, k-veto, veto, and Borda voting rules, maximin, Copeland α for every α ∈ [0,1], and simplified Bucklin voting rules. Hence, in this work, we discover a fundamental vulnerability in using minimax regret based approach in partial preferential setting and propose a novel way to tackle it.

In this paper, we study a maximum likelihood estimation (MLE) approach to voting when the set of alternatives has a multi-issue structure, and the voters' preferences are represented by CP-nets.We first consider general multi-issue domains, and study whether and how issue-by-issue voting rules and sequential voting rules can be represented by MLEs. We first show that issue-by-issue voting rules in which each local rule is itself an MLE (resp. a candidate scoring rule) can be represented by MLEs with a weak (resp. strong) decomposability property. Then, we prove two theorems that state that if the noise model satisfies a very weak decomposability property, then no sequential voting rule that satisfies unanimity can be represented by an MLE, unless the number of voters is bounded.We then consider multi-issue domains in which each issue is binary; for these, we propose a general family of distance-based noise models, of which give an axiomatic characterization. We then propose a more specific family of natural distance-based noise models that are parameterized by a threshold. We identify the complexity of winner determination for the corresponding MLE voting rule in the two most important subcases of this framework.

The performance of generalized correlation (GC) methods for time-delay estimation when a priori knowledge of the received source spectrum is limited is improved. The treatment is restricted to finite-time observation of a single low-pass source, where the uncertainty in its autospectrum is characterized by a single unknown parameter. The constrained processor (CP) selects an optimum postcorrelator filter from a finite set of alternatives that are designed to span the expected range of source spectra. An approach proposed previously for this situation is the LMS adaptive filtering method for time delay estimation (LMSTDE). For purposes of comparison, both the theoretical and simulation performance of the LMSTDE method are examined. Simulation experiments indicate that LMSTDE offers performance comparable to conventional GC methods without a priori knowledge of the source spectrum. The CP in the same setting, however, can yield significantly lower variance time delay estimates than either the LMSTDE or conventional GC methods, with performance approaching the Cramer-Rao lower bound. >

We consider optimization via simulation over a finite set of alternatives. We employ a Bayesian value-ofinformation approach in which we allow both correlated prior beliefs on the sampling means and correlated sampling. Correlation in the prior belief allow us to learn about an alternative’s value from samples of similar alternatives. Correlation in sampling, achieved through common random numbers, allows us to reduce the variance in comparing one alternative to another. We allow for a more general combination of both types of correlation than has been offered previously in the Bayesian ranking and selection literature. We do so by giving an exact expression for the value of information for sampling the difference between a pair of alternatives, and derive new knowledge-gradient methods based on this valuation. 1

The functions used by different optimization methods are interpreted with expected utility viewpoint. It makes possible to distinguish two groups of methods - criterion and functional choice ones. The first group of methods sets preferences on the values of the criteria, and the second - on the values of the functions presenting the preferences of decision maker on the scales of attributes. Such an interpretation of functions that does not depend on how they are created, allowed considering methods of multi-criteria optimization and multi-dimensional utility from unified positions. The analytic hierarchy process uses the priority function calculated based on the matrix of pairwise comparisons. So, it is related to the group of methods of functional choice too. The resulting system allows one to compare their methods for quality and evaluate the effectiveness of tasks solving.

An Interactive Approach to Alternative Ranking Involving Inverse Decision Aiding

The problem of sequential change diagnosis is considered, where a sequence of independent random elements is accessed sequentially, there is an abrupt change in its distribution at some unknown time, and there are two main operational goals: to quickly detect the change and to accurately identify the post-change distribution among a finite set of alternatives. A standard algorithm is considered, which does not explicitly address the isolation task and raises an alarm as soon as the CuSum statistic that corresponds to one of the post-change alternatives exceeds a certain threshold. It is shown that in certain cases, such as the so-called multichannel problem, this algorithm controls the worst-case conditional probability of false isolation and minimizes Lorden’s criterion, for every possible post-change distribution, to a first-order asymptotic approximation as the false alarm rate goes to zero sufficiently faster than the worst-case conditional probability of false isolation. These theoretical results are also illustrated with a numerical study.

We investigate the problem of finding the minimum number of queries needed to perfectly identify an unknown quantum gate within a finite set of alternatives, considering both deterministic strategies. For unambiguous gate discrimination, where errors are not tolerated but inconclusive outcomes are allowed, we prove that parallel strategies are sucient to identify the unknown gate with minimum number of queries and we use this fact to provide upper and lower bounds on the query complexity. In addition, we introduce the notion of generalized t-designs, which includes unitary t-designs and group representations as special cases. For gates forming a generalized t-design we prove that there is no dierence between perfect probabilistic and perfect deterministic gate discrimination. Hence, evaluating of the query complexity of perfect discrimination is reduced to the easier problem of evaluating the query complexity of unambiguous discrimination. 1998 ACM Subject Classification J.2 Physical sciences and engineering

This note examines the complexity of solving the bicriterion vector maximum problem and the associated linear-weighted criterion problem over a finite set of alternatives. It presents an algorithm for linear-weighted problems with separable objectives that is considerably more efficient than complete enumeration of all alternatives and shows that the algorithm is essentially optimal for this problem.

We study strategic negotiation models featuring costless delay, general recognition procedures, endogenous voting orders, and finite sets of alternatives. Two examples show: 1. non-existence of stationary subgame-perfect equilibrium (SSPE). 2. the recursive equations and optimality conditions are necessary for SSPE but insufficient because these equations can be singular. Strategy profiles excluding perpetual disagreement guarantee non-singularity. The necessary and sufficient conditions for existence of stationary best responses additionally require either an equalizing condition or a minimality condition. Quasi SSPE only satisfy the recursive equations and optimality conditions. These always exist and are SSPE if either all equalizing conditions or all minimality conditions hold.

The paper deals with a possible solution to the problem of choosing the best variant of a simulation model from a finite set of alternatives in the process of decision-making support. Evaluation of possible solutions is carried out via methods of multi-criteria analysis of alternatives. The integration of simulation models and models of decision support is set-theoretically formalized. The problem of choosing the rational set of simulation model parameters, considering restrictions imposed by experts, is solved by heuristic optimization method based on the local search strategy. Developed algorithms and software form a separate module in the decision support system (DSS) "Space" that makes it possible to rank alternatives submitted by simulation models. DSS software architecture is developed by means of object-oriented paradigm and is built of C# and T-SQL code. Combined with client-server model via thin-client architecture it gives additional flexibility to the users due to their option preferences of hardware and software. DSS “Space” allows ranking of simulation results using both traditional methods, such as weight and multiplicative function, ideal value and fuzzy and hybrid models of user’s preferences identification.Designed software allows applying it for variable scientific and technical civil and military problems due to its universality.

We model the problem of managing capacity in a build-to-order environment as a Brownian drift control problem and seek a policy that minimizes the long-term average cost. We assume the controller can, at some cost, shift the processing rate among a finite set of alternatives, for example by adding or removing staff, increasing or reducing the number of shifts, or opening or closing production lines. The controller incurs a cost for capacity per unit time and a delay cost that reflects the opportunity cost of revenue waiting to be recognized or the customer service impacts of delaying delivery of orders. Furthermore, he incurs a cost per unit to reject orders or idle resources as necessary to keep the workload of waiting orders within a prescribed range. We introduce a practical restriction on this problem, called the 𝒮-restricted Brownian control problem, and show how to model it via a structured linear program. We demonstrate that an optimal solution to the 𝒮-restricted problem can be found among a special class of policies called deterministic nonoverlapping control band policies. These results exploit apparently new relationships between complementary dual solutions and relative value functions that allow us to obtain a lower bound on the average cost of any nonanticipating policy for the problem, even without the 𝒮 restriction. Under mild assumptions on the cost parameters, we show that our linear programming approach is asymptotically optimal for the unrestricted Brownian control problem in the sense that by appropriately selecting the 𝒮-restricted problem, we can ensure its solution is within an arbitrary finite tolerance of a lower bound on the average cost of any nonanticipating policy for the unrestricted Brownian control problem.