Individual choice behavior: A theoretical analysis.

“Having rank-distance determine the difficulty of comparison (or odds of choosing incorrectly) is commonly assumed in econometrics and psychometrics as well (e.g., as in the Luce-Shepard choice model (Luce 1959; Shepard 1959)).”

“We show that this implies that not all trembling hand perfect Nash equilibria are robust and not all robust equilibria are perfect.”

“– 146 – 1) The multinomial logit model can be compatible with the sequential choice model, as the Luce model (Luce, 1959) suggested.”

“also includes various models that rely on Luce's (1959) choice”

“Each neuron is activated with the Softmax function [24, 25].”

“[10] was the first to use the multinomial logit model in theoretical analysis of individual choice behavior and provided a key component to the multinomial logit with the influential independence of irrelevant alternatives (IIA).”

“In fact CE is based on Random Utility Models (RUMs) (Luce, 1959; Manski, 1977; McFadden, 1974; Thurstone, 1927; Yellott, 1977), which assume that utility is derived from the properties/ characteristics of goods/services rather than directly from the goods themselves.”

“(2010), Tyson (2008), and Manzini et al. (2013). 7That is, an alternative x is chosen when compared to another alternative y , and y is chosen when compared to a third alternative z, but z is chosen when compared to x. For experimental findings, see Tversky (1969), Loomes et al.”

“However, we will highlight this as a potential limitation in Section 5, as it is not possible to determine whether any effect on performance was present.”

“Standard models of action selection posit that the probability of selecting action Ai with estimated value μ̂i 665 follows a softmax function [105, 106]: 666 p(Ai) = ei ∑ j e βμ̂j , (15) where β is referred to as the inverse temperature parameter.”

“alters the value of the two superior options, and can thus be classified as ‘irrational’ [5].”

“Under the Luce condition, we have p(x|B) = p(x|X)∑ z∈B p(x”

“Most notably the epsilon-greedy strategy consists of choosing a random lever with epsilon-frequency, and otherwise choosing the lever with the highest estimated mean [51], and the soft-max strategy [52] which an arm is sampled according to a distribution that is an estimate of its performance (we refer the reader to t…”

“Assuming that follows a type-I extreme value distribution (Luce 2005) this yields the probability that performer j is preferred by evaluator i”

“One of the most widely used models for this purpose is the Bradley-Terry-Luce (BTL) model [8, 20], which predicts Pij , the probability of choosing Ti over Tj , as a function associated with the true ratings of the two stimuli:”

“…(1953) and Debord (1987b), – Multiple criteria decision making using “ordinal information” (see Arrow and Raynaud, 1986; Roy, 1991), in view of the results in Bouyssou (1996), – Psychology with, e.g., the study of binary choice probabilities (see Luce, 1959; Suppes, Krantz, Luce and Tversky, 1989).”

“LASR’s buffer-based memory addresses one of the early criticisms of models based on associative chains. In LASR, repeated elements of the same type are represented separately with a distinct trace (i.e., repeated elements are given separate memory slots). As a result, LASR has no difficulty learning a simple sequence…”

“The accuracy of the model in selecting the next element was calculated as the activation of the target output unit divided by the total activation of all output units, commonly referred to as the Luce choice ratio (hereafter LCR; Luce, 1959).”

“The reward function R̂θ is trained using a pair-wise ranking loss [38] based on the Luce-Shephard choice rule [39]:”

“Finally, D-REX learns via Equation 3 the reward function through supervised learning on the trajectories’ rankings, using a pairwise ranking loss according to Luce-Shepard rule [20].”

“Extensive theoretical, computational, and empirical evidence has documented clear non-linearities in how representations of the actual probability distributions used as evidence to generate a response map onto the generated response (Luce, 2005; Tversky, 1967; Ungemach, Chater, & Stewart, 2009).”

“…Retrieval consists of activating the representation of the test exemplar and allowing it to pass activation, via the semantic units, to the representations in LTM and using the Luce (1959) choice axiom to retrieve these active LTM representations into working memory (WM) (see Doumas et al., 2008).”

“When only choices are modeled, and with certain restrictions on its parameters, the LBA is a random utility model, similar to the multinomial logit (Luce choice) model (Luce, 1959; Marley & Flynn, in press).”

“This form of loss function follows from the classic Bradley-Terry and Luce-Shephard models of preferences (Bradley & Terry, 1952; Luce, 2012) and has been shown to be effective for training neural networks from preferences (Christiano et al., 2017; Ibarz et al., 2018).”

“of the BTL-model (Bradley and Terry, 1952; Luce, 1959 ), yielding scale values for each type of transposition.”

“The soft-max rule is foundational in economics, decision theory, and cognitive psychology (Luce, 1959, 1977), and we first selected it for this problem on the basis of a completely independent set of experiments (Frank, Goodman, Lai, & Tenenbaum, 2009).”

“Then, the user response to a sub-query qi is probabilistic based on Luce’s Choice Axiom [38], [39] which is a widely used human decision model in cognitive science as it nicely captures the uncertainty in humans’ choices: P (ai|qi,mi, w) = exp(Rmi(q ai i )) exp(Rmi(q ai i )) + exp(Rmi(q āi i )) (2) This models probab…”

“We assume that nodes choose their actions according to the logit choice model which captures bounded rationality prevalent in human decision-making [35, 36], and consider the notion of quantal response equilibrium (QRE) [37] as the solution concept.”

“To model noise in agent decisions, we incorporate a noisy rational model, a widely used human decision model in cognitive science [19]–[21], into our proposed framework.”

“The logistic choice rule has often been used to model choices under uncertainty (e.g. Luce, 1959).”

“The aim of this work is to propose such an analytic method that is able to take traffic information into account to explore the mechanism of route choice behavior.”

“Softmax methods are based on Luce’s axiom of choice [57] and pick each item for recommendation with a probability that is proportional to its average reward.”

“Drawing on Thurstone’s work, Luce [13] formulated models of discrete probabilistic choice, i.e., random utility models.”

“Important contributions to the discrete choice analysis have been made by, among others, Luce (2005) and McFadden (1980).”

“The CE method has its theoretical grounding in Lancaster’s model of consumer choice [33] and its econometric basis in random utility theory [34,35].”

“The choice of rule Z depends on the stochastic procedure based on the nonlinear Luce (1959) ratio: Pi eU i n j eU j n (5) where Pi denotes the probability that rule i will be selected, and j reflects all rules within response set .”

“Most theories of utility, including the RWU one described in Marley and Luce (2001), have either explicitly or implicitly assumed idempotence. Luce and Marley (2000) present some theoretical results for non-idempotent binary gambles. To our knowledge, no related theoretical work has been done on failures of idempotenc…”

“moral dilemmas to broader contexts shows parallels with the development of choice theory (Luce, 1959).”

“Score based models [12], on the other hand, are very efficient as they divide permutation construction into stages and assign scores on each stage such that the final probability is a combination (multiplication) of stage-wise scores.”

“Still, already May [53] has shown that cyclic preferences were not extraordinary (violating transitivity of the preference relation), and Luce [51] noted that people sometimes seem to choose one alternative over another with a given consistent probability not equal to one (violating completeness of the preference rela…”

“Several methods for modeling rank data have been proposed, including the Bradley-Terry-Luce model (Bradley and Terry, 1952; Luce, 1959), the Mallows model (Mallows, 1957) and the Plackett-Luce model (Plackett, 1975; Luce, 1959).”

“note f1;2;:::;ng, i2[n] denote the i-th robot in a fleet of n robots, and it H 2[n] denote the robot controlled by the user at time t. We assume the user selects robot it H using the Luce choice model [12], P[ it H =]= e f(s t i ) n å j=1 f(s j ); (1) where f : S !R is the user’s scoring function, and st i is the state…”

“The Bradley-Terry model was later generalized by Plackett and Luce to a model for permutations [23, 27].”

“A major exception is the extensive series of papers on the utility of gambling that develops representations involving a relatively standard idempotent representation, plus a weighted entropy-type term; these results are summarized in Luce et al. (2009).”

“Rather, we draw from Luce’s Choice Axiom [7] to model the probability with which users choose each option, in combination with a softmax rule [26], formalized as follows.”

“Given a top-1 ranking dataset, the total order of N items can be learned through the Plackett-Luce (PL) model (Luce, 2012).”

“Most models of animal and human multi-attribute choice make the implicit assumption that an individual’s preference for a particular item does not change when irrelevant items are added to the choice set (Luce 1959; Rapoport 1989).”

“The choice axiom implies the existence of a cardinal utility scale. THEOREM 5.1 ( Luce 1959 /2005).”

“Interested readers should refer to Luce (2005) for a detailed description of a logit model and Hensher, Rose, and Greene (2005) for a details of a probit model.”

“The rank ordering model based on extreme value distributions is sometimes called the Plackett-Luce model, as an extension of the multinomial logit choice model of Luce (1959) to rank orderings.”

“Given how natural the problem of rank aggregation is, there has been a wide body recent [1], [2] and classical work [3]–[6] to understand how to consistently combine preferences.”

“Hence, we adopted anm-alternative forced-choice task [10, 33, 36, 53] that is an expansion of the two-alternative forced-choice task.”

“This decoy (or “asymmetric dominance”) effect clearly violates the “axiom of regularity” of rational choice theory: when given a choice set A, where A⊂B, the probability of choosing an element x from B cannot be greater than the probability of choosing x from A (Luce, 1959; Yang, 2013).”

“Popular choice models usually applied in market simulations are the BTL (Bradley and Terry, 1952), a constant utility model which uses a probabilistic choice rule (Luce, 1959), and the MNL (McFadden, 1974), a random utility model with a deterministic choice rule (Baltas et al, 1997).”

“We represent preferences for Bl and B2 by it and (l-7t) respectively (0<7t<l); and assume that, in the absence of promotion, consumers choose between brands with probabilities proportional to preferences (Luce, 1959).”