Generalized Goal Programming: polynomial methods and applications

The concept of distance rationalizability allows one to define new voting rules or "rationalize" existing ones via a consensus class of elections and a distance. A candidate is declared an election winner if she is the consensus candidate in one of the nearest consensus elections. It is known that many classic voting rules are defined or can be represented in this way. In this paper, we focus on the power and the limitations of the distance rationalizability approach. We first show that if we do not place any restrictions on the class of consensus profiles or possible distances then essentially all voting rules become distance-rationalizable. Thus, to make the concept of distance ratioanalizability meaningful, we have to restrict the class of distances involved. To this end, we present a very natural class of distances, which we call votewise distances. We investigate which voting rules can be rationalized via votewise distances and study the properties of such rules and study their relations with rules that are maximumlikelyhood estimators.

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“…For example, R n + -monotonic norms are used in a similar context in non-preemptive goal programming (Carrizosa & Fliege, 2002).…”

Section: Stv Is Not Votewise Distance-rationalizablementioning

confidence: 99%

Distance rationalization of voting rules

Elkind

Faliszewski²,

Slinko

2015

Soc Choice Welf

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“…(The numerator 31 in one of the fractions in Equation (21) as found in Nesterov and Nemirovskii [30] is obviously a typo, as the proof of the corresponding proposition immediately shows.) For lower bounds on this number, the reader is referred to Carrizosa and Fliege [4]. Obviously, for large , the leading term √ ln in the estimate above has the coefficient 1/ 1 − 1 , so it makes sense to maximize 1 − 1 .…”

Section: Algorithm 1 (Stage I)mentioning

confidence: 98%

“…For more details about different scalarization techniques, the reader is referred to Fliege [7,8], Hillermeier [20], Carrizosa and Fliege [4], and Jahn [24]. Introducing artificial variables, we see that we have to consider an infinite family of scalar problems of the form…”

Section: Scalarizationmentioning

confidence: 99%

“…The warm-start approach presented in this subsection is put to heavy use in what follows, and the corresponding algorithmic method is generalized to scalar programs with quadratic objective functions in §2.3 and to arbitrary smooth convex scalar programs in §2. 4 in the parameter space is proposed ( §3.2) and analyzed ( §3.3). The latter contains the main result of the paper; it turns out that due to the warm-start technique introduced in §2.2, the theoretical complexity of this algorithm is lower than the naïve approach of using a prespecified number of parameter values to achieve a certain density of approximation in the image space n of the multicriteria optimization problem considered.…”

Section: Scalarizationmentioning

confidence: 99%

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An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems

Fliege

2006

Mathematics of OR

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In multicriteria optimization, several objective functions have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multicriteria optimization problem, where the objective functions involved are arbitrary convex functions and the set of feasible points is convex. The method is based on generating warm-start points for an efficient interior-point algorithm, while the approximation computed consists of a finite set of discrete points. Polynomialtime complexity results for the method proposed are derived. In these estimates, the number of operations per point decreases when the number of points generated for the approximation increases. This reduced theoretical complexity estimate is a novel feature and is not observed in standard solution techniques for multicriteria optimization problems.

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“…As noted in Carrizosa and Fliege (2002), it is interesting to note that solving (P x ) is equivalent to solve the following problem…”

Section: Preliminariesmentioning

confidence: 99%

On a robustness property in single-facility location in continuous space

Ciligot-Travain

Traoré

2012

TOP

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We consider a single-facility location problem in continuous space, here the problem of minimizing a sum or the maximum of the possibly weighted distances from a facility to a set of points of demand. The main result of this paper shows that every solution (optimal facility location) of this problem has an interesting robustness property. Any optimal facility location is the most robust in the following sense: given a suitable highest admissible cost, it allows the greatest perturbation of the locations of the demand without exceeding this highest admissible chosen cost.

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Generalized Goal Programming: polynomial methods and applications

Cited by 24 publications

References 44 publications

Distance rationalization of voting rules

Distance rationalization of voting rules

An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems

On a robustness property in single-facility location in continuous space

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