Abstract:

Individuals behave with choice probabilities defined by a multinomial logit (MNL) probability distribution over a finite number of alternatives which includes utilities as parameters. The salient feature of the model is that probabilities depend on the choice-set, or domain. Expanding the choice-set decreases the probabilities of alternatives included in the original set, providing positive probabilities to the added alternatives. The wider probability 'spread' causes some individuals to fur- ther deviate from their higher valued alternatives, while others find the added alternatives highly valuable. For a population with diverse preferences, there ex- ists a subset of alternatives, called the optimum choice-set, which balances these considerations to maximize social welfare. The paper analyses the dependence of the optimum choice-set on a parameter which specifies the precision of individuals' choice ('degree of rationality'). It is proved that for high values of this parame- ter the optimum choice-set includes all alternatives, while for low values it is a singleton. Numerical examples demonstrate that for intermediate values, the size and possible nesting of the optimum choice-sets is complex. Governments have various means (defaults, tax/subsidy) to directly a''''ect choice probabilities. This is modelled by 'probability weight'parameters. The paper analyses the structure of the optimum weights, focusing on the possible exclusion of alternatives. A binary example explores the level of 'type one'and 'type two'errors which justify the imposition of early eligibility for retirement benefits, common to social security systems. Finally, the e''''ects of heterogeneous degrees of rationality among individuals are briefly discussed.

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