Optimal Communication-Distortion Tradeoff in Voting Debmalya Mandal - PowerPoint PPT Presentation

Nov 21, 2022 •260 likes •309 views

Optimal Communication-Distortion Tradeoff in Voting Debmalya Mandal (Columbia), Nisarg Shah (UofT), and David Woodruff (CMU) Optimal Communication-Distortion Tradeoff in Voting Debmalya Mandal (Columbia), Nisarg Shah (UofT), and David Woodruff

Optimal Communication-Distortion Tradeoff in Voting Debmalya Mandal (Columbia), Nisarg Shah (UofT), and David Woodruff (CMU)
Optimal Communication-Distortion Tradeoff in Voting Debmalya Mandal (Columbia), Nisarg Shah (UofT), and David Woodruff (CMU) ‣ Social Welfare : ∑ ∑ (a) [Voting] (b) [ -selection] v i ( a ) max a ∈ S v i ( a ) k i i
Optimal Communication-Distortion Tradeoff in Voting Debmalya Mandal (Columbia), Nisarg Shah (UofT), and David Woodruff (CMU) ‣ Social Welfare : ∑ ∑ (a) [Voting] (b) [ -selection] v i ( a ) max a ∈ S v i ( a ) k i i Maximum sw with v ‣ Distortion ( dist ( f ) ): max Expected sw of f on v v ‣ Communication ( ): No. of bits reported by each voter C ( f )
Optimal Communication-Distortion Tradeoff in Voting Debmalya Mandal (Columbia), Nisarg Shah (UofT), and David Woodruff (CMU) ‣ Social Welfare : ∑ ∑ (a) [Voting] (b) [ -selection] v i ( a ) max a ∈ S v i ( a ) k i i Maximum sw with v ‣ Distortion ( dist ( f ) ): max Expected sw of f on v v ‣ Communication ( ): No. of bits reported by each voter C ( f ) ‣ Optimal communication for a desired distortion : d Elicitation Voting -Selection k Θ ( m / d ) Θ ( m /( kd ) ) Deterministic ˜ ˜ Θ ( m / d 3 ) Θ ( m /( kd 3 ) ) Randomized ˜ ˜

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