Weekly Economics Seminar by Souvik Roy
October 16, 2019 @ 1:30 pm - 2:40 pm
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Title: On the Equivalence of Ordinal Bayesian Incentive Compatibility and Dominant Strategy Incentive Compatibility for Random Rules
Speaker: Souvik Roy, Associate Professor, Indian Statistical Institute, Kolkata
Abstract: We study random voting mechanisms and establish an equivalence relation between ordinal Bayesian incentive compatible (OBIC) random mechanisms and dominant strategy incentive compatible (DSIC) random mechanisms. We show that almost every locally ordinal Bayesian incentive compatible(LOBIC) random rule on a domain satisfying elementary monotonicity (as defined in Mishra (2016)) is also locally dominant strategy incentive compatible(LDSIC). It follows from our result that almost every (with probability 1) OBIC and elementary monotonic random rule on unrestricted, single-peaked, single-crossing, single-dipped domain is DSIC. We further provide a sufficient condition on the domains where under unanimity almost all LOBIC rules are tops-only. As it turns out most well-known domains like the unrestricted domain, single-peaked domains, single-crossing domains and single-dipped domains satisfy our sufficient condition. We also show that under OBIC, unanimity implies elementary monotonicity on the unrestricted domain.