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The axiomatic foundation of logit

Breitmoser, Yves (2016): The axiomatic foundation of logit.

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Abstract

Multinomial logit is the canonical model of discrete choice but widely criticized for requiring specific functional assumptions as foundation. The present paper shows that logit is behaviorally founded without such assumptions. Logit's functional form obtains if relative choice probabilities are independent of irrelevant alternatives and invariant to utility translation (narrow bracketing), to relabeling options (presentation independence), and to changing utilities of third options (context independence). Least squares differs from logit only by making the additional assumption that utility is perceived to be quadratic around the utility maximizer, showing that logit is the more general model and least squares actually requires specific functional assumptions. Reviewing behavioral evidence, presentation and context independence seem to be violated in typical experiments, not IIA. Relaxing context independence yields contextual logit (Wilcox, 2011), relaxing presentation independence allows to capture "focality" of options.

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