Computational social choice

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Computational social choice is a field at the intersection of

manipulation, and issues arising from the problem of representing
and eliciting preferences in combinatorial settings.

Winner determination

The usefulness of a particular

Kemeny-Young method, Dodgson's method, and Young's method are all NP-hard problems.[4][5][6][7] This has led to the development of approximation algorithms and fixed-parameter tractable algorithms to improve the theoretical calculation of such problems.[8][9][10]

Hardness of manipulation

By the

manipulated in the sense that voters can sometimes achieve a better outcome by misrepresenting their preferences, that is, they submit a non-truthful ballot to the voting system. Social choice theorists have long considered ways to circumvent this issue, such as the proposition by Bartholdi, Tovey, and Trick in 1989 based on computational complexity theory.[11] They considered the second-order Copeland rule (which can be evaluated in polynomial time), and proved that it is NP-complete for a voter to decide, given knowledge of how everyone else has voted, whether it is possible to manipulate in such a way as to make some favored candidate the winner. The same property holds for single transferable vote.[12]

Hence, assuming the widely believed hypothesis that P ≠ NP, there are instances where polynomial time is not enough to establish whether a beneficial manipulation is possible. Because of this, the voting rules that come with an NP-hard manipulation problem are "resistant" to manipulation. One should note that these results only concern the worst-case: it might well be possible that a manipulation problem is usually easy to solve, and only requires superpolynomial time on very unusual inputs.[13]

Other topics

Tournament solutions

A tournament solution is a rule that assigns to every tournament a set of winners. Since a preference profile induces a tournament through its majority relation, every tournament solution can also be seen as a voting rule which only uses information about the outcomes of pairwise majority contests.[14] Many tournament solutions have been proposed,[15] and computational social choice theorists have studied the complexity of the associated winner determination problems.[16][1]

Preference restrictions

Restricted preference domains, such as

Condorcet paradox and thus can circumvent impossibility results like Arrow's theorem and the Gibbard-Satterthwaite theorem.[17][18][19][20] From a computational perspective, such domain restrictions are useful to speed up winner determination problems, both computationally hard single-winner and multi-winner rules can be computed in polynomial time when preferences are structured appropriately.[21][22][23][24] On the other hand, manipulation problem also tend to be easy on these domains, so complexity shields against manipulation are less effective.[22][25] Another computational problem associated with preference restrictions is that of recognizing when a given preference profile belongs to some restricted domain. This task is polynomial time solvable in many cases, including for single-peaked and single-crossing preferences, but can be hard for more general classes.[26][27][28]

Multiwinner elections

While most traditional voting rules focus on selecting a single winner, many situations require selecting multiple winners. This is the case when a fixed-size parliament or a committee is to be elected, though multiwinner voting rules can also be used to select a set of recommendations or facilities or a shared bundle of items. Work in computational social choice has focused on defining such voting rules, understanding their properties, and studying the complexity of the associated winner determination problems. See multiwinner voting.

See also

References

  1. ^
    ISBN 9781107060432
    .
  2. S2CID 1927244
    .
  3. ^ Brill, Markus; Fischer, Felix (2012-01-01). "The Price of Neutrality for the Ranked Pairs Method". Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence. AAAI'12: 1299–1305.
  4. ^
    S2CID 154114517
    .
  5. doi:10.1016/j.tcs.2005.08.031
    .
  6. S2CID 367623
    .
  7. S2CID 3205730
    .
  8. doi:10.1016/j.artint.2012.04.004
    .
  9. S2CID 5674305
    .
  10. ISBN 9783540688655
    .
  11. S2CID 16158098
    .
  12. S2CID 17749613
    .
  13. doi:10.1609/aimag.v31i4.2314
    .
  14. doi:10.1137/0133030
    .
  15. ^ Laslier, Jean-François (1997). Tournament Solutions and Majority Voting. Springer Verlag.
  16. ^ Moon, John W. (1968-01-01). Topics on tournaments. Holt, Rinehart and Winston.
  17. S2CID 153953456
    .
  18. S2CID 153683957
    .
  19. ISBN 978-0300186987
    .
  20. doi:10.1016/0022-0531(69)90020-9
    .
  21. ^ Elkind, Edith; Lackner, Martin; Peters, Dominik (2016-07-01). "Preference Restrictions in Computational Social Choice: Recent Progress" (PDF). Proceedings of the 25th International Conference on Artificial Intelligence. IJCAI'16: 4062–4065.
  22. ^
    hdl:1802/10425
    .
  23. S2CID 2839179
    .
  24. S2CID 5348844
    .
  25. doi:10.1016/j.ic.2010.09.001
    .
  26. arXiv:1602.08109 [cs.GT
    ].
  27. doi:10.1006/jagm.1994.1010
    .
  28. ISBN 9781586038915
    .

External links

  • The COMSOC website, offering a collection of materials related to computational social choice, such as academic workshops, PhD theses, and a mailing list.
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