[EM] new working paper: "Four Condorcet-Hare hybrid methods for single-winner elections"
Dear Election Methods Fans, I've been working on a paper entitled "Four Condorcet-Hare hybrid methods for single-winner elections", which I'd like to submit to Voting Matters sometime in the near future, and I'd really appreciate your comments and feedback. Here is a link to the current draft: http://www.econ.ucsb.edu/~armytage/hybrids.pdf Here is the abstract: I examine four single-winner election methods, denoted here as Woodall, Benham, Tideman, and Smith-Hare, which each make use of both Condorcet?s pairwise comparison principle and the plurality elimination principle used in Hare?s single transferable vote system. I find that these methods have many significant properties in common, including Smith efficiency and relatively strong resistance to strategic manipulation, though they differ slightly with regard to minor criteria such as ?Smith-IIA? and ?mono-add-plump?. Here are the non-technical definitions for the four methods: Woodall Score candidates according to the Hare (IRV) elimination order, and chose the Smith set candidate with best score. That is, define each candidate?s Hare score as the round in which he is eliminated by the Hare method. (The Hare winner is not eliminated, so we set his score to the number of candidates.) If the Smith set has only one member, then this is the Woodall winner; otherwise, the winner is the candidate from inside the Smith set with the best Hare score. Benham Eliminate the plurality loser until there is a Condorcet winner. That is, if there is a Condorcet winner, he is also the Woodall winner. Otherwise, the method eliminates the candidate with the fewest first choice votes, and checks to see whether is a candidate who beats all other non-eliminated candidates pairwise. This process repeats until there is such a candidate, who is then declared the winner. Smith-Hare Eliminate candidates not in the Smith set, and then conduct a Hare tally among remaining candidates. Tideman Alternate between eliminating all candidates outside the Smith set, and eliminating the plurality loser, until one candidate remains. That is, as in Smith-Hare, we begin by eliminating all candidates outside the Smith set. If this leaves only one candidate (a Condorcet winner), then he is elected. Otherwise, we eliminate the candidate with the fewest first choice votes. Then, we recalculate the Smith set, and eliminate any candidates who were in it before but are no longer in it as a result of the plurality loser elimination. These two steps repeat until only one candidate (the winner) remains. I do something like a substantially scaled-down version of the analysis from my Strategic Voting and Nomination paper -- the aim is to effectively make the point that these methods are quite resistant to strategy, without letting the analysis take over the whole paper. For those who want more details on the analysis, I suggest the big SVN paper. I should also mention that the reason that a few rows in my tables are blank is because I'm still waiting on the results of those simulations. All right, well, I hope that some of you enjoy the paper, and/or find it informative, and I look forward to your comments. my best, James Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] electing a variable number of seats
On Fri, Feb 18, 2011 at 7:54 AM, Juho Laatu wrote: > If you want to keep this property, the approach proposed by Michael Rouse > could determine > the number of board members. If most votes go to few candidates, then there > would be 5 members > (with different weight). If the votes are more distributed, then all > candidates (up to 9 candidates) > that get support over some agreed limit would be elected. Alternatively one > could use the number > of unrepresented votes as the criterion on how many members to elect. This > approach would > improve proportionality and keep the size of the board small at the same time. You could still use PR-STV to give a proportional result. There is a formula which defines the "effective number of parties". It is also used in economics to define how many firms there are in a market. The formula is 1/sum((vote share squared)) So, if the first choice totals were A: 20% B: 30% C: 15% D: 12% E: 18% F: 5% The result gives: 1/(0.2*0.2 + 0.3*0.3 + 0.15*0.15 + 0.12*0.12 + 0.18*0.18 + 0.05*0.05) = 4.96 This says that there are around 5 groups in the vote, which is about right. If the voters were less concentrated, you get a larger number A: 8% B: 12% C: 7% D: 14% E: 6% F: 10% G: 9% H: 11% I: 4% K: 19% would give 8.56 The rule could be that you use that formula using the first choice votes and round to the nearest whole number between 5 and 9. Also, a property of the formula is that if the votes are exactly evenly distributed, then the number will be equal to the number of candidates. For example, if there were 8 candidates and each got exactly 1/8 of the vote, then the number of seats would be equal to 8. You can then use standard PR-STV with that number as the seats target. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] electing a variable number of seats
Hi Charlie, In terms of improving proportionality why not keep this system (which I feel is not a bad one for electing a smallish board) why not introduce specific seats reserved for specific groups, for instance you could say that a minimum of 50% of seats are reserved for women so for example if 8 candidates achieve more than 50%+1 but only 3 of the winning candidates are women, then only 6 seats can actually be filled. Of course this raises issues, but if your organisation has already accepted that proportionality is important enough to dictate the election system then I don't see the problem. Paddy. From: Charlie DeTar To: jgilm...@globalnet.co.uk Cc: election-methods@lists.electorama.com Sent: Fri, 18 February, 2011 0:38:44 Subject: Re: [EM] electing a variable number of seats On 02/17/2011 07:21 PM, James Gilmour wrote: > Charlie > I see two problems here. > > 1. You do not give the conditions under which the constitution of this >organisation allows the number of board members to be > varied. > > 2. More importantly, someone needs to define the purpose of this election a >great deal better. Who would have the power to add one > extra winner with a view to "improving representation" and who would decide >what "improved representation" might be? And just who > exactly would have the power to reduce the number elected board members with > a >view to "eliminating polarizing candidates" and who > would decide that the last winner was a "polarizing candidate" who should be >excluded? Valid points. Currently, the bylaws allow between 5 and 9 board members. The current process is that each member is voted on individually by simple majority of the voting members of the organization. With this process, it's clear when the number changes: if only 5 candidates receive 50+% of the vote, there are only 5 board members; if 9, then there are 9. There is not currently any defined process for what happens when (a) fewer than 5 people receive 50% of the vote, or (b) more than 9 people do; in the history of the organization it hasn't happened. This is one aspect in which the current system is broken I share your concerns with allowing an individual to have the authority to define when to grow or shrink the board. However, if there were a voting system that could quantify questions like how well the electorate is represented, or whether a candidate is polarizing, the system could select the mix of candidates which would produce an optimal score according to those metrics. If my language here sounds more like it comes from a machine learning world, that's because that's closer to my experience. Thanks very much Markus and others for the sources and recommendations, I'll look into those. best, Charlie Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
