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

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]

∑

i

vi(a) ∑

i

max

a∈S vi(a) k

Optimal Communication-Distortion Tradeoff in Voting

Debmalya Mandal (Columbia), Nisarg Shah (UofT), and David Woodruff (CMU)

• Social Welfare:

(a)

[Voting] (b) [ -selection]

∑

i

vi(a) ∑

i

max

a∈S vi(a) k

• Distortion (

): dist(f )

max

v

Maximum sw with v Expected sw of f on 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]

∑

i

vi(a) ∑

i

max

a∈S vi(a) k

• Distortion (

): dist(f )

max

v

Maximum sw with v Expected sw of f on v

• Communication (

): No. of bits reported by each voter

C(f )

Elicitation Voting

• Selection

Deterministic Randomized

˜ Θ (m/d) ˜ Θ (m/d3) ˜ Θ (m/(kd)) ˜ Θ (m/(kd3))

k

• Optimal communication for a desired distortion :

d