False Name Proof and Anonymity in Voting Systems, Study notes of Computers and Information technologies

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False‐name‐proof vo/ng

Malvika Rao Haoqi Zhang

Agenda

• What is false‐name‐proof?
• Why important? Why hard?
• A nega/ve result
• Some fairly posi/ve results
• Discussion and future work

Good idea, serious implica/ons

• One voter cannot benefit from cas/ng 2 same votes
• => If 2 voters vote the same way, only one of the votes can maNer in choosing outcome
• Example: 1000 people prefer A over B 1 person prefers B over A => Same as 1 person who prefers A and one who prefers B => Not very responsive to voter preferences!

Think about vo/ng rules we know

• Borda
• Plurality
• Cup
• STV They will all break!
• ….
• …. Warning. Outlook does not look good….

Let’s think about some possible rules

• Choose a candidate uniformly at random to be the winner - Doesn’t use votes at all, so it is a (weak) dominant strategy to do anything. - Thus, is anonymity proof.

Let’s think about desirable outcomes

• If everyone prefers A to B, we like to select A over B
• If everyone prefers A over all other outcomes, we had like to select A - Turns out even this is not possible with more than 2 candidates with anonymity‐proof!

Why care about anonymity–proof?

• Anonymity‐proof implies that we don’t need the iden//es of the voters
• Convenient for voters
  • No need for registra/on
  • No privacy concerns
  • Leads to more par(cipa(on and response
• Quan for organizer
  • Publicity, respect
  • $$$ from votes
  • Adver/sing

2 approaches

1. What vo/ng protocols are anonymity‐proof?
2. Can we impose addi/onal condi/ons to achieve anonymity‐proofness and s/ll be responsive to votes? (e.g., introduce cost for vo/ng) Do #1 first: Vincent Conitzer, Annoymity‐Proof Vo2ng Rules Paper from WINE 2008

Defini/on: Neutral

• A vo/ng rule is neutral if it treats all alterna/ves symmetrically
• Implica/ons:
  • If no votes, must select each alterna/ve with equal probability
  • If votes are {a>b, b>a}, must give equal probability to a and b.

Defini/on: False‐name‐proof

• A vo/ng rule is false‐name‐proof if for each voter, the expected u/lity from cas/ng one (true) vote is >= the expected u/lity from cas/ng mul/ple votes.

Defini/on: Anonymity‐proof

• A vo/ng protocol is anonymity‐proof if it is false‐name‐proof and voluntary

Main result

• Given: a neutral, anonymity‐proof vo/ng rule
• Outcome: the rule will choose a winner by:
  • assigning some probability k to choosing an alterna/ve at random
  • assigning probability 1‐k to draw a pair of alterna/ves at random - If every vote prefers the same alterna/ve between the two, choose that alterna/ve - Otherwise, flip a coin to decide between the two

Order of business

• The proof is quite interes/ng and the results are fairly surprising.
• We will go through the proof in some detail, by first shrinking the vote set and then by characterizing the single vote case.
• I will try to give intui/on and avoid as much nota/on and algebra as possible
• Please stop me with ques/ons!

Lemma 1

• Consider v = a 1 > … > a k > B > a k+ > … > a l
• Consider v’ that agree with ranking in v everywhere except in B
• Lemma: For anonymity‐proof vo/ng rule, adding v’ doesn’t change the probability of a i winning