A revised law of comparative judgment

Bayesian locally optimal design of knockout tournaments

“…This type of advantage can be modeled in the Thurstone-Mosteller model as an additive effect following Harris (1957); when i and j compete on the home field of i, a home-field advantage parameter η increases the probability of a win for i by letting…”

Paired comparison experiments involving all possible pairs

“…The maximum likelihood estimators (p, 9 , O ) of (n, y, v ) satisfy In paired comparison experiments arising in the area of marketing research, order effect parameters are usually considered to be nuisance parameters which complicate the analysis, but which must be accounted for within the analysis or by randomization of the order of presentation in order to avoid biases in the estimates of the worth parameters. On the other hand, in paired comparison experiments arising in psychology, the 'order' of the items in a pair may represent a spatial or a temporal positional effect, and the order effect may be more important to the experimenter than the relative worth parameters themselves, since the stimuli are often controlled by the experimenter in these situations (see Harris, 1957). Within this second context, we examine the relative efficiency of two design configurations in testing for 'significant order effects and for differences among the item-worth parameters.…”

“…Models reflecting the presence of order effects in paired comparison experiments have appeared in the literature. Harris (1957) has modified the Thurstone-Mosteller (see Mosteller, 1951) model by assuming the existence of an additive.order effect parameter which has the effect of increasing or decreasing the mean difference in response to the items being compared, depending upon whether the effect of the order of presentation enhances the worth of the first or the second of the items presented. Beaver & Gokhale (1975) produced a model to account for order effects by introducing an additive order effect parameter into the Bradley-Terry (1952) model, while Davidson & Beaver (1977) produced a multiplicative order effect model in the presence of ties using the Davidson (1970) and Rao-Kupper (1967) extensions of the Bradley-Terry model which allow for the occurrence of ties.…”

Optimal design of factorial paired comparison experiments in the presence of within-pair order effects

“…Augustin (2004) provides further support for the superiority of the model involving multiplicative order effects, and Fienberg (1979) re-examines the multiplicative order-effects model from a technical viewpoint. Harris (1957) presented a constant additive bias model, which is similar to that of Davidson and Beaver (1977) except that it is based on the Thurstone (1927) model (see, e.g., Critchlow & Fligner, 1991). Davidson and Beaver (1977) find evidence of order effects in the weights-judging experiment mentioned above, as well as in an experiment involving different food mixes.…”