We develop interactive algorithms to find a strict total order for a set of discrete alternatives for two different valuefunctions: linear and quasiconcave. The algorithms first construct a preference matrix and then...
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We develop interactive algorithms to find a strict total order for a set of discrete alternatives for two different valuefunctions: linear and quasiconcave. The algorithms first construct a preference matrix and then find a strict total order. Based on the ordering, they select a meaningful pair of alternatives to present the decision maker (DM) for comparison. We employ methods to find all implied preferences of the DM, after he or she makes a preference. Considering all the preferences of the DM, the preference matrix is updated and a new strict total order is obtained until the termination conditions are met. We test the algorithms on several instances. The algorithms show fast convergence to the exact total order for both valuefunctions, and eliciting preference information progressively proves to be efficient.
We investigate in a simple bi-criteria experimental study, whether subjects are consistent with a linear value function while making binary choices. Many inconsistencies appeared in our experiment. However, the impact...
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We investigate in a simple bi-criteria experimental study, whether subjects are consistent with a linear value function while making binary choices. Many inconsistencies appeared in our experiment. However, the impact of inconsistencies on the linearity vs. non-linearity of the valuefunction was minor. Moreover, a linear value function seems to predict choices for bi-criteria problems quite well. This ability to predict is independent of whether the valuefunction is diagnosed linear or not. Inconsistencies in responses did not necessarily change the original diagnosis of the form of the valuefunction. Our findings have implications for the design and development of decision support tools for Multiple Criteria Decision Making problems. (C) 2012 Elsevier B.V. All rights reserved.
We compare five different prediction methods (linear estimated weights, AHP weights, equal weights, logistic regression, and a lexicographic method) in their success rate for predicting preferences in pairwise choices...
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We compare five different prediction methods (linear estimated weights, AHP weights, equal weights, logistic regression, and a lexicographic method) in their success rate for predicting preferences in pairwise choices. Students were asked to make pairwise comparisons between student apartments on four criteria: size, rent, travel time to the university and travel time to a (hobby) location of their choice. First ten choices were used to set up the estimation model, and subsequent ten choices are used for prediction. We find that the linear estimation method has the highest prediction success rate. Furthermore, the probability of predicting a choice correctly differs only slightly (by 0.1) between linear consistent and inconsistent subjects, ie. subjects whose preferences were consistent or inconsistent with a linear value function. This shows that in the absence of other preference information, a linear value function is suitable for prediction purposes. (C) 2016 Elsevier B.V. All rights reserved.
We investigate the connection between weights, scales, and the importance of criteria, when a linear value function is assumed to be a suitable representation of a decision maker's preferences. Our considerations ...
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We investigate the connection between weights, scales, and the importance of criteria, when a linear value function is assumed to be a suitable representation of a decision maker's preferences. Our considerations are based on a simple two-criteria experiment, where the participants were asked to indicate which of the criteria was more important, and to pairwise compare a number of alternatives. We use the participants' pairwise choices to estimate the weights for the criteria in such a way that the linear value function explains the choices to the extent possible. More specifically, we study two research questions: (1) is it possible to find a general scaling principle that makes the rank order of the importance of criteria consistent with the rank order of the magnitudes of the weights, and (2) how good is a simple, direct method of asking the decision maker to "provide" weights for the criteria compared to our estimation procedure. Our results imply that there is reason to question two common beliefs, namely that the values of the weights would reflect the importance of criteria, and that people could reliably "provide" such weights without estimation.
We show how a standard tool from statistics --- namely confidence bounds --- can be used to elegantly deal with situations which exhibit an exploitation-exploration trade-off. Our technique for designing and analyzing...
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We show how a standard tool from statistics --- namely confidence bounds --- can be used to elegantly deal with situations which exhibit an exploitation-exploration trade-off. Our technique for designing and analyzing algorithms for such situations is general and can be applied when an algorithm has to make exploitation-versus-exploration decisions based on uncertain information provided by a random process. We apply our technique to two models with such an exploitation-exploration trade-off. For the adversarial bandit problem with shifting our new algorithm suffers only O((ST)1/2) regret with high probability over T trials with S shifts. Such a regret bound was previously known only in expectation. The second model we consider is associative reinforcement learning with linear value functions. For this model our technique improves the regret from O(T3/4) to O(T1/2).
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