Download presentation

Presentation is loading. Please wait.

Published bySophie Paskett Modified over 3 years ago

1
How to Rig Elections and Competitions Noam Hazon*, Paul E. Dunne +, Sarit Kraus*, Michael Wooldridge + + Dept. of Computer Science University of Liverpool United Kingdom *Dept. of Computer Science Bar Ilan University Israel

2
Outline A common way to aggregate agents preferences - voting But it can be manipulated! Current models assume perfect information We analyzed a model of imperfect information Theoretically, manipulation is hard: NP-Complete proofs Practically it is not: Heuristics and experimental evaluation Conclusion, Future work

3
Why Voting? Preference aggregation - to a socially desirable decision Not only agents… Human decisions among a collection of alternatives Sport tournaments But it can be manipulated if we have perfect information By a single voter or a coalition of voters By the election officer

4
Our Model - Imperfect Information Agenda rigging by the election officer Linear order Tree order Complexity results Verifying an agenda is in P Finding a perfect agenda seems to be hard Empirical results Easy-to-implement heuristics performed well Tested against random and real data Motivation - better design of voting protocols

5
Set of outcomes/candidates, Imperfect information ballot matrix M, Voting trees Basic Definitions ABCD CA C CD B AB C A

6
Linear Order Tree Verifying an agenda is O(n 2 ) - with dynamic programming A candidate can only benefit by going late in an order And this is not true for general trees! Finding an order for a particular candidate to win: With a non-zero probability - O(n 2 ) With at least a certain probability

7
Weak Version of Rigged Agenda A run - An order agenda together with the intended outcomes P[r | M] - a probability that the run will result in our candidate WIIRA Problem - Set of candidates, Ω Imperfect information matrix, M A favored candidate, ω* A probability p Is there a run in which the winner is ω*, s.t. P[r | M] p ? NP-C, from the k-HCA problem on tournaments

8
Balanced Tree Order Verifying an agenda is O(n 2 ) Finding an order for a particular candidate to win: With a non-zero probability - open problem [Lang07] With at least a certain probability - NP-C [Vu08]

9
From Theory to Practice Concern: It might be that there are effective heuristics to manipulate an election, even though manipulation is NP-complete. Discussion: True. The existence of effective heuristics would weaken any practical import of our idea. It would be very interesting to find such heuristics. [Bartholdi89]

10
Linear Order – Conversion Probabilistic data deterministic data Simple convert Threshold convert Not better than random order ω3ω3ω2ω2ω1ω1 0.60.7- ω1ω1 -0.3 ω2ω2 - 0.4 ω3ω3 ω3ω3ω2ω2ω1ω1 01- ω1ω1 1-0 ω2ω2 -00 ω3ω3

11
General Approach Heuristics: Far adversary.... Best win Local search Random order Two data sets: Random data- uniform and normal distribution Real data - 29 teams from the NBA, top 13 tennis players ω*ω*m-1m-212

12
Linear Order- Normal Distribution

13
Linear Order- 13 Tennis Players

14
Balanced Tree- Normal Distribution

15
Balanced Tree- 13 Tennis Players

16
Balanced Tree- 29 NBA Teams

17
Conclusion Two voting protocols with incomplete information Agenda verification is in P Manipulation by the officer seems to be hard Far adversary, best win and local search can help a lot! Future: other voting protocols {hazonn,sarit}@cs.biu.ac.il, {mjw,ped}@csc.liv.ac.uk

Similar presentations

OK

Manipulating the Quota in Weighted Voting Games (M. Zuckerman, P. Faliszewski, Y. Bachrach, and E. Elkind) Presented by: Sen Li Software Technologies.

Manipulating the Quota in Weighted Voting Games (M. Zuckerman, P. Faliszewski, Y. Bachrach, and E. Elkind) Presented by: Sen Li Software Technologies.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on body language in communication Ppt online downloader for games Ppt on biography of william shakespeare Ppt on biotechnology in india Ppt on electricity generation from solar energy Ppt on nature and human quotes Ppt on production possibility curve Ppt on mind reading computer free download Ppt on new product development steps Ppt online open channel