Re: [EM] Condorcet Ties
It was asked: What are the most acceptable forms of tie breaking other than random, that might be used before random in the case of Condorcet Voting. I mean actual ties in voting preferences and not merely failure to have a Condorcet approved candidate. I reply: So you're not talking about circular tie solutions, but rather about actual pairwise ties, or equal defeats, right? SSD has a version that I've called Cloneproof SSD, or Small Committee SSD. It's equivalent to what Markus Schulze proposes for small committee votes. Norman Petry prefers it too. You've been to the electionmethods website, and so I don't need to define SSD here. Cloneproof SSD is SSD with a different stopping rule. Instead of declaring a winner as soon as there's an unbeaten candidate, Cloneproof SSD stops declares a winner when there are no cycles in the current Schwartz set. Whoever is unbeaten at that time wins. Now, about the ties you asked about: Sometimes, in a small committee, there will be several defeats that are equally the weakest defeats in the current Schwartz set. We've defined the weakest defeat as the one with least support. In other words, if A beats B, then the defeat's support is the number of people ranking A over B. But if there are 2 or more defeats that are equally the weakest in the current Schwartz set, as measured in that way, then drop the one that has the most opposition. The opposition to A's defeat of B is the number of people ranking B over A. If there are more than one defeat in the current Schwartz set that have the same support and the same opposition, then drop all of those simultaneously. Above, I said "Whoever is unbeaten at that time wins." But what if more than one candidate wins? Then delete from the rankings every candidate other than those unbeaten ones, and repeat the count, from the start, with those reduced rankings. Repeat until doing so fails to reduce the number of winners. When that happens, choose among the winners by Random Ballot, or Chairman Ballot (decide in advance which it will be). Random ballot means that you choose a ballot from the election at random, and whichever of the winners is highest ranked on that ballot wins the election. Of course if the winners are all ranked equal on that ballot, then you pick another random ballot, till you get one that solves the tie. Chairman Ballot is the same as Random Ballot, except that the chairman's ballot is always used to solve those ties. Of course if the chairman's ballot ranks the winners equally, then use Random Ballot. The above method is agreed by several people on EM to be the best way to count ranked ballots for a single-winner choice, in small committees where ties are likely. (In public elections, where ties are quite rare, it doesn't matter how they're solved. If there's a tiebreaker already on the books, the reform legislation could just say to use it, where I here said to use Random Ballot or Chairman Ballot. As has been pointed out, and as I demonstrated here, Cloneproof SSD is equivalent to BeatpathWinner. I claim that Cloneproof SSD's definition is more naturally obviously motivated justified, but BeatpathWinner makes for a briefer computer program, and a somewhat faster-running program. That shouldn't ordinarily be important, and I consider Cloneproof SSD's better plausibility more important. But you might want to use BeatpathWinner to implement Cloneproof SSD, if brevity of the computer program, and minimum running time are important. Of course it would be quite rare for there to be so many candidates voters for running time to be significant. ps. Also, I notice that the EM webpage does not list Condorcet as a voting system, but rather lists Minmax as the name of the system.. Blake Cretney calls his website the EM resource website. Blake's website isn't officially authorized as that, unless I'm mistaken. "Minmax" is vague, as exemplified by Blake defining it in a way different from how it's usually used here. Blake's website is really just Blake's website. Unless I'm mistaken, Rob hasn't designated it the official EM resource website. But Rob, tell me if I'm mistaken on that. Blake's website contains some criteria definitions that act contrary to how people expect those criteria to act. Additionally, there may be one or more vaguely-defined criteria there too. Blake's advocacy, at his website, of margins, as opposed to defeat-support, is _not_ representative of opinion at this website. but with a different type of counting (Minmax as described there goes for a minimum score rather than for a maximum score as described at http://electionmethods.org/) Is there another name for Condorcet voting Some call PC "Minmax". I prefer PC, because "Minmax" can mean too many different things.
Re: [EM] Condorcet Ties
Hi, I'm Forest. When you say "ties in voting preferences," I take it you are talking about the individual voter filling out the ballot, and not knowing what to do if he has no real preference in the case of two of the candidates. Is that right? The answer to this question is that some versions require you to express preferences anyway, so in that case you would do best to flip a coin, and hope that someone else who doesn't care also flips a coin and cancels out your "preference." Other rules allow voters to express the preferences they care about, and leave the rest unexpressed. Does that help? Forest On Mon, 19 Feb 2001, Moe St. EverGreen wrote: What are the most acceptable forms of tie breaking other than random, that might be used before random in the case of Condorcet Voting. I mean actual ties in voting preferences and not merely failure to have a Condorcet approved candidate. ps. Also, I notice that the EM webpage does not list Condorcet as a voting system, but rather lists Minmax as the name of the system.. but with a different type of counting (Minmax as described there goes for a minimum score rather than for a maximum score as described at http://electionmethods.org/) Is there another name for Condorcet voting, and is Condorcet voting currently considered the best option for a single winner race?
RE: [EM] Condorcet Ties
There are any number of ways to break ties. While the simplest, and in some ways the most intuitive way to break ties is random, you can get more complex by adding other election methods. For instance, conduct a Borda count, or an IRV runoff. There are alot to choose from. I think Borda is probably a good one. A simpler method would be to do a plurality count (the candidate with the most number 1 votes) - this is just as good, fairly easy to count, and somewhat intuitive - that is, if two candidates are evenly split between the electorate, which candidate is more voters' favourite? Some Condorcet methods use a number of different strategies to decide between candidates. If they are pairwise tied, give them a Copeland score (2 points for a head to head victory, 1 for a draw and none for a loss). If they're tied because you've used minmax or something and both candidates largest defeats are equally small, then do a pairwise count between them. The pairwise count between the candidates should always be the first tie breaker, if it isn't the cause of the tie. Basically, if you're satisfied that you have a very good election method, then tie breakers are much of a muchness. My suggestion would be - do a pairwise count first. If the candidates are still tied, then do a plurality count (most number of number 1's). -Original Message- From: Moe St. EverGreen [mailto:[EMAIL PROTECTED]] Sent: Tuesday, 20 February 2001 5:52 To: [EMAIL PROTECTED] Subject: [EM] Condorcet Ties What are the most acceptable forms of tie breaking other than random, that might be used before random in the case of Condorcet Voting. I mean actual ties in voting preferences and not merely failure to have a Condorcet approved candidate. ps. Also, I notice that the EM webpage does not list Condorcet as a voting system, but rather lists Minmax as the name of the system.. but with a different type of counting (Minmax as described there goes for a minimum score rather than for a maximum score as described at http://electionmethods.org/) Is there another name for Condorcet voting, and is Condorcet voting currently considered the best option for a single winner race?
Re: [EM] Condorcet Ties
On Mon, 19 Feb 2001 13:52:14 -0500 "Moe St. EverGreen" [EMAIL PROTECTED] wrote: What are the most acceptable forms of tie breaking other than random, that might be used before random in the case of Condorcet Voting. I mean actual ties in voting preferences and not merely failure to have a Condorcet approved candidate. If you don't want to use random, I think it's a good idea designate one person as the tie breaker. You can set up some rather complicated rules to break ties based on the ballots, but these generally don't make much sense, and don't give any result in the most common situations (like a simple two-way tie). ps. Also, I notice that the EM webpage does not list Condorcet as a voting system, but rather lists Minmax as the name of the system.. but with a different type of counting (Minmax as described there goes for a minimum score rather than for a maximum score as described at http://electionmethods.org/) That's my unofficial Election-Methods Resource site: http://www.fortunecity.com/meltingpot/harrow/124 I recommend that anyone who wants to know what Condorcet actually recommended should read Condorcet. He is of course most famous for recommending that the pairwise unbeaten candidate should win. This is called the Condorcet winner, and some people refer to Condorcet's method as just this procedure. Of course this method is prone to ties. So, some people on this list chose a convenient Condorcet completion method, which they called Condorcet (EM) or Condorcet. That electionmethods.org site calls it Plain Condorcet. I call this Condorcet (EM) on my site. In academic journals, choosing the least defeated seems to be called Minmax. I use this name for the method where the strength of a defeat is decided by the margin. You'll notice that Condorcet (EM) decides strength of a defeat by votes on the winning side. Other than that, it's the same method. The procedure given for Plain Condorcet on electionmethods.org is equivalent to what I call Condorcet (EM), even though this may not be obvious. Is there another name for Condorcet voting, and is Condorcet voting currently considered the best option for a single winner race? That's a little like asking which religion is considered the best. The short answer is, it depends who you ask (as well as what you mean by "Condorcet"). My preference is for Ranked Pairs, which is a Condorcet completion method detailed at: http://www.fortunecity.com/meltingpot/harrow/124 There's even a (low activity) list set up for discussing it. --- Blake Cretney
Re: [EM] Condorcet Ties
"Moe St. EverGreen" wrote: Is there another name for Condorcet voting, and is Condorcet voting currently considered the best option for a single winner race? There are several variations of Condorcet-like methods, which could be lumped together under the category "pairwise methods". As for your second question, it depends who you talk to. Among participants on this list, some appear to favor one or more of the pairwise methods, and some (including myself) lean toward approval voting. Bart Ingles
