<br><br>
<div class="gmail_quote">On Tue, May 31, 2011 at 6:06 PM, Kristofer Munsterhjelm <span dir="ltr"><<a href="mailto:km_elmet@lavabit.com">km_elmet@lavabit.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">Peter Zbornik wrote:<br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">
<div>
<div></div>
<div class="h5">Juho,<br> summarize my argument concerning generalized ballot and generalized ballot completion and in the end of this email I suggest a new single-member Condorcet election system.<br> Nomenclature: I think that "null-candidate" (marked "X") is a fitting name for voting for not filling a seat. The other names given do not have that chique mathematical sound: "White", "None of the Above", "Re-open nominations", "Ficus (the plant)", etc.<br>
In the discussion, I think I showed the following<br>If blank voting ("null candidates") is not allowed, then truncated/incomplete ballots give different election results for winning votes and for margins.<br>Compare Kevin Venzke's example:<br>
35:A>B<br>25:B<br>40:C<br>If we complete this election (Woodall's original proposal) to<br>35:A>B>C<br>25:B>A=C<br>40:C>A=B,<br>then the election gives different results whether the candidates in the ties are resolved as 0.5 vs 0.5 (margins - A winner) or 0 vs 0 (winning votes - B winner)<br>
(compare the results of the election at <a href="http://condorcet.ericgorr.net/" target="_blank">http://condorcet.ericgorr.net/</a> and <a href="http://www1.cse.wustl.edu/~legrand/rbvote/calc.html" target="_blank">http://www1.cse.wustl.edu/~legrand/rbvote/calc.html</a>)<br>
For margins, Woodall's plurality criterion is violated.<br> If the same election is completed to allow for blank voting:<br>35:A>B>X>C<br>25:B>X>A=C<br>40:C>X>A=B,<br>then the election gives same result (B - winner) both for margins and for winning votes and the parwise comparison matrix will be identical for both methods if a an equality awarded 0.5 votes for both candidates.<br>
Thus, truncated/incomplete ballots can be completed using the following generalized symmetric ballot completion algorithm, in order to give same election results for margins and winning votes and to not violate Woodall's plurality criterion for margins:<br>
1. add s "null candidates" under the ranked candidates, where s is the number of seats<br>2. rank the unranked candidates equally and under the "null candidate".<br>3. equalities are resolved by giving each candidate 0.5 votes in the pairwise comparison.<br>
If margins are used in Condorcet elections with generalized symmetric ballot completion, then Woodall's plurality criterion is not violated, since the "blank votes" are actually represented and the ballot is complete.<br>
</div></div> Maybe the entry in Wikipedia could be updated, where we read "Only methods employing winning votes satisfy Woodall's plurality criterion <<a href="https://mail.google.com/wiki/Plurality_criterion" target="_blank">https://mail.google.com/wiki/Plurality_criterion</a>>."
<div class="im"><br><a href="http://en.wikipedia.org/wiki/Condorcet_method#Defeat_strength" target="_blank">http://en.wikipedia.org/wiki/Condorcet_method#Defeat_strength</a><br> I think an equality on the ballot between two candidates A=B should intuitively mean nothing else than giving half a vote to A>B and B>A, i.e. the pairwise comparison matrix should not change and Woodall's plurality criterion should be kept at the same time. This is only possible if the generalized symmetric ballot completion algorithm is used.<br>
The rule of requiring the candidate to score more than 50% in a pairwise comparison which I proposed in a previous email is enforced if generalized symmetric completion is used.<br></div></blockquote><br>How would you deal with Condorcet cycles? Is the rule "must score more than 50% in at least one comparison"? If not, there could be problems when no beats-all winner exists. </blockquote>
<div> </div>
<div>See later posts. Especially the recent email to Juho.</div>
<div> </div>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">
<div class="im"><br><br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">If we use generalized ballot completion, then the null-candidate wins in a Condorcet election (but not in an IRV election):<br>
45:A>X>B<br>40:B>X>A<br>15:X>A=B<br>Woodall's plurality criterion is not violated because X is not a candidate to win a seat.<br> Introducing a cutoff, like saying that "a winning candidate needs to be explicitly ranked on 50% of the ballots" maybe is equivalent to the generalized ballot completion algorithm (I don't know). However such a cutoff doesn't allow for ranking between disfavoured alternatives, which the generalized ballot does.<br>
</blockquote><br></div>It seems you've rediscovered the concept of an approval cutoff, but in another context. There are two sorts of approval cutoff: implied and explicit. In the former case, truncation means that you don't want those you didn't rank to win. In the latter, there's an explicit mark - your X - after which the same holds true.<br>
<br>Implied cutoff methods are less expressive but they can guard against burial. Kevin Venzke shows how this works in Condorcet//Approval: you can't effectively bury a candidate because ranking him last means you give him approval, which strengthens his position. I imagine that like with explicit cutoff, you could bury more powerfully by saying something like A>B>D>X>C instead of a honest A>B>C>D (or strategic A>B>D>C).</blockquote>
<div> </div>
<div>Maybe I misunderstand something. If I truncate A>B>D, then this is completed to A>B>D>C with C disapproved and buried.</div>
<div>X is just the cutoff, so I really don't see how burying would be more powerful.</div>
<div> </div>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid"><br>As for whether X wins whenever the winner is not ranked above him on a majority of the ballots, that would be a majority version of the Pareto criterion. "If a majority ranks A above B, then B must not win". But we know that it's possible for a majority to rank A above B, another majority rank B above C, and a third majority rank C above A. Therefore I don't think it's equivalent, although I can't find an example.<br>
(In other words, a winning candidate could be not-X even when X is ranked above him by a majority, but then this candidate must be in a cycle with X.) </blockquote>
<div> </div>
<div>Yes, there are two rules, see later posts.</div>
<div> </div>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">
<div class="im"><br><br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">I aggree that it is better to require the voter to rank all candidates, as an incomplete ballot is completed in any case and the voter might not know the ballot completion algorithm.<br>
</blockquote><br></div>On the other hand, forcing voters to rank all candidates can lead them to taking the easy way out - in the short term by donkey-voting and in the long term by encouraging (or at least not resisting) a change of the ballots to include above-the-line voting. Both of these things have happened in Australia, where the type of IRV they use means that voters have to rank every candidate, and the consequence is that the parties wield greater power. </blockquote>
<div> </div>
<div>Yes, several other shorthand ranking formulas/algorithms are thinkable so that the voter would save time and ink from writing less on the ballot, but that is really concerning only the execution of the elections. I would rather not focus on this issue in this discussion.</div>
<div> </div>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">
<div class="im"><br><br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">I don't think that introducing a null candidate in a Condorcet election has any impact on its violation of Later-no-harm, i.e..the incentive of the voter to bullet-vote to maximize the success of "His" candidate. Even if the equalities and null candidates would be disallowed on the ballot, later-no-harm would still not hold for Condorcet elections and burying would still be an efficient strategy (slightly OT: the claim that Condorcet methods elect centrist canidates is questionable, since the centrist candidate will be the prime target for burying attempts, since he/she has the highest chance of winning, thus losing his "centricity" even before it is measurable in a election).<br>
</blockquote><br></div>I think I found out earlier that to immunize completely against burial, you'd need both LNHarm and LNHelp, because there are two ways burial could work, and one is blocked by LNHarm whereas the other is blocked by LNHelp. The Condorcet criterion is incompatible with both, in any event.</blockquote>
<div> </div>
<div>OK, noted.</div>
<div> </div>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid"><br>Your OT would probably hold no matter what tendency Condorcet has. Say that Condorcet tends to elect winners of type K. Then type-K candidates are the most visible targets, and thus could be buried if the electorate is strategic enough.
<div class="im"><br><br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">Some ideas:<br>An other interesting issue, is if election systems with several election election rounds can improve results in Condorcet elections, for instance, an STV Condorcet election could be held with three seats.<br>
Those who get one of the seat go through to the second round (which maybe can be automatical), where one of the candidates is elected in a Condorcet election, where a Condorcet winner is guaranteed.<br> Maybe an election type could be devised which makes a bottom-up proportional ranking. At the start of the election, as many seats as there are candidates are elected, then in each subsequent round one candidate is dropped util we have a Condorcet winner. <br>
</blockquote><br></div>I have a hunch (as you put it :-) that you can't both have Droop proportionality and monotonicity. My conjecture is based on that the apportionment/party list version of these methods (largest remainder Droop) fails population-pair monotonicity, i.e. transferring votes from one party to another can in some cases make the former party gain seats. I have not been able to prove this, but if I'm right, that means that runoff methods based on STV (even Condorcet STV, if it passes the Droop proportionality criterion) would be nonmonotone.<br>
<br>Further, such methods wouldn't be cloneproof. To slightly alter an example of Woodall's, consider:<br><br>700: x<br>300: y<br> 1: z<br><br>and two winners should elect x and y. </blockquote>
<div> </div>
<div>Not if we use static quotas as I propose.</div>
<div>
<div>Droop quota is >1001/3=333.67, so y doesn't pass.</div></div>
<div>If we append the Xs as I propose then the ballots are (it's not really needed)</div>
<div>700: x>NULL<br>300: y>NULL<br> 1: z>NULL<br></div>
<div>x is elected and the other seat is left vacant.</div>
<div>x's voters are stupid not to add a second candidate (the clone below).<br></div>
<div> </div>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">But now clone x:<br><br>350: x>x'<br>350: x'>x<br>300: y<br> 1: z<br><br>Then the DPC forces the two winners to be x and x', so cloning can push other candidates out of the runoff. Perhaps a better runoff algorithm would be something akin to LeGrand's minmax approval. Minmax approval picks the set of candidates for which the candidate who disagrees the most about the composition of the council, as measured by Hamming distance, disagrees the least. I'm unsure how to generalize it, however. </blockquote>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">
<div class="im"><br><br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">Do you or anyone else around on this list have a reference to where the debate between IRV and Condorcet stands today (pros and cons of the methods respectively)?<br>
Personally I am not yet convinced that Condorcet is a "better method" than IRV when it comes to resisting tactical voting.<br></blockquote><br></div>I don't have a reference. You're probably right that IRV in general resists strategy better than does the ordinary Condorcet methods discussed on this list (like Schulze, Minmax, or Tideman); but note that James Green-Armytage's paper shows Smith-limited IRV to be as good as, if not better than, ordinary IRV with respect to strategy resistance, while always choosing winners from the Smith set (and thus always electing the CW where it exists).<br>
<br>His working paper is here: <a href="http://www.econ.ucsb.edu/~armytage/hybrids.pdf" target="_blank">http://www.econ.ucsb.edu/~armytage/hybrids.pdf</a><br><br>(One does pay for this resistance by having a method that fails monotonicity, though.)<br>
</blockquote>
<div> </div>
<div>I will check it out.</div></div><br>