On Random Social Choice Functions With The Tops-Only Property

We study the standard voting model with randomization. A Random Social Choice Function (or RSCF) satisfies the tops-only property if the social lottery under each preference profile depends only on voters' peaks of preferences. We identify a general condition on domains of preferences (the Interior Property and the Exterior Property) which ensures that every strategy-proof RSCF satisfying unanimity has the tops-only property. We provide applications of this sufficient condition and use it to derive new results.

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