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Why settle for quadratic? Why not cubic? Or why not n^1.2? What's so special about quadratic that makes it the best candidate?
by jude- 5y ago
Why settle for quadratic? Why not cubic? Or why not n^1.2? What's so special about quadratic that makes it the best candidate?
- ghancock 5y agoIt incentivizes the welfare-maximizing result. I don’t have a short “intuitive” explanation of why handy but the math is covered in section 8.3 of Public Choice III (should be easy to get in college libraries, pdf copies can be found online if needed).
- nickvincent 5y agoThe core argument for x^2 is basically just that it's the only function with linear derivative, so for rational voters who calculate marginal benefit of additional votes purchased at cost x^2 (in terms of likelihood of changing the outcome of the "election"), you get a welfare maximizing outcome. There's some assumptions underlying the theoretical result, but there's also a lot active experimentation in the real world, a few links: https://www.radicalxchange.org/concepts/quadratic-voting/ https://www.radicalxchange.org/concepts/quadratic-voting/, https://en.wikipedia.org/wiki/Quadratic_voting https://en.wikipedia.org/wiki/Quadratic_voting Here's what I believe is the key paper on the topic https://www.aeaweb.org/articles?id=10.1257/pandp.20181002 https://www.aeaweb.org/articles?id=10.1257/pandp.20181002 (appendix: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2790624 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2790624) Lalley, Steven P., and E. Glen Weyl. 2018. "Quadratic Voting: How Mechanism Design Can Radicalize Democracy." AEA Papers and Proceedings, 108: 33-37.
- tgv 5y ago> rational voters That's a rather ridiculous assumption, isn't it? I still remember the 3rd year psychology university student, who asked: "What's a square root?"
- nabla9 5y agoRationality expectation is good if irrationality of others does not harm rational voter.
- tgv 5y agoIn this case, a well-organized and mathematically adept voter can and will harm less rational ones, thus skewing the balance instead of restoring it.
- im3w1l 5y agoThis is a good objection. The system might be so complicated that people don't understand how to correctly express their preferences.
- nickvincent 5y agoDefinitely a challenge for many mechanism design approaches to intervening in the world. As I understand, the only really solution is to experiment in the real world, see what holds and see what doesn't, and tweak accordingly (e.g. test out different interfaces that communicate how the mechanism works!)
- timdaub 5y agoActually it's a good point and IMO for a population that may have a certain distribution of voting credits e.g. shareholders of a stock, adjusting the exponent can make sense to more fairly distribute power.
- bo1024 5y agoThere are a few mathematical reasons. I forget the details, but I remember that a key point is to consider marginal cost: the derivative of a quadratic is linear. I think the Central Limit Theorem is also relevant, as someone else here pointed out. Anyway, if you really want to know, you can read the papers!