Template-type: ReDif-Paper 1.0 Author-Name: Peters, H.J.M. Author-workplace-name: Quantitative Economics Author-Name: Roy, S. Author-workplace-name: Quantitative Economics Author-Name: Sadhukhan, S. Author-Name: Storcken, A.J.A. Author-workplace-name: Quantitative Economics Title: An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains Abstract: We show that every strategy-proof and unanimous probabilistic rule on a binary restricted domain has binary support, and is a probabilistic mixture of strategy-proof and unanimous deterministic rules. Examples of binary restricted domains include several types of single-dipped domains, the single-peaked domain where peaks are restricted to two adjacent alternatives, and the single-crossing domain with two tops. We also provide some extensions to infinitely many alternatives. Series: GSBE Research Memoranda Creation-Date: 20160101 Number: 012 File-URL: https://cris.maastrichtuniversity.nl/ws/files/1338625/guid-dbfbace9-02b5-40b2-8dde-9d51a4cebaa4-ASSET1.0.pdf File-Format: application/pdf File-Size: 488998 Handle: Repec:unm:umagsb:2016012 DOI: 10.26481/umagsb.2016012