Choice procedure consistent with similarity relations

Abstract

We deal with the approach, initiated by Rubinstein, which assumes that people, when evaluating pairs of lotteries, use similarity relations. We interpret these relations as a way of modelling the imperfect powers of discrimination of the human mind and study the relationship between preferences and similarities. The class of both preferences and similarities that we deal with is larger than that considered by Rubinstein. The extension is made because we do not want to restrict ourselves to lottery spaces. Thus, under the above interpretation of a similarity, we find that some of the axioms imposed by Rubinstein are not justified if we want to consider other fields of choice theory. We show that any preference consistent with a pair of similarities is monotone on a subset of the choice space. We establish the implication upon the similarities of the requirement of making indifferent alternatives with a component which is zero. Furthermore, we show that Rubinstein's general results can also be obtained in this larger class of both preferences and similarity relations.

Salience Theory of Choice Under Risk

“…We are not the first to propose a model of context dependent choice among lotteries. Rubinstein (1988), followed by Aizpurua et al (1990) and Leland (1994), builds a model of similarity-based preferences, in which agents simplify the choice among two lotteries by pruning the dimension (probability or payoff, if any), along which lotteries are similar. The working and predictions of our model are different from Rubinstein's, even though we share the idea that the common ratio Allais paradox (see Section 5.1.2) is due to subjects' focus on lottery payoffs.…”

A Vague Theory of Choice over Time

“…For instance, the σ − δ model cannot account for 'size effects' of the following type: suppose that δ = .7 and σ = 1, so that (9, 0) is preferred to (10, 1) but (10, 3) is preferred to (9, 2), so that preference reversal occurs 15 . Suppose now we double the stakes, and thus look at comparisons between (18, 0) and (20,1), and between (18,2) and (20,3). Now it is easy to verify that the σ − δ models predicts a preference for the smaller, earlier amount in both comparisons, and preference reversal no longer occurs 16 .…”

“…To see this latter point, contrast the example above with the prediction the β − δ model. The initial preferences would be translated in the following requirements: z > βδ 2 x βδy > z βδ 2 x > βδy ⇔ δx > y 13 An alternative way of describing the decision tree is to consider the corresponding time dependent set of alternatives. Initially (at time 0) the set of alternatives that can be 'seen' is A 0 = {(z, 0) , (y, 1) , (x, 2)}.…”

“…In the last decade an alternative model, which is consistent with this type of evidence, has enjoyed considerable prominence and success in the literature. This is the model of hyperbolic discounting (HDM) 2 , in which the discount factor is a hyperbolic function of time. The central point of this approach is that the rate of time preference between alternatives is not constant but varies, and in particular decreases, with the passage of time.…”

“…See Fishburn and Rubinstein[7] 2. See for instance Phelps and Pollack[18], Loewenstein and Prelec[13], Laibson[12], Frederick et al[8], O'Donoghue and Rabin[15],[16].…”