<html><head><meta http-equiv="Content-Type" content="text/html charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">Here's one example that is quite different from the previous one, but still somehow in line with my "crusade against negative votes and default better than bottom votes" :-) .</div><div class=""><br class=""></div><div class="">First preferences are 35:A, 35:B, 30:C. Preference orders are mixed. Opinion space is thus not linear.</div><div class=""><br class=""></div><div class="">Most A, B and C supporters reject their competitors in the hope of disqualifying them based on rule 2. There are more bullet voters among A and B supporters than among C supporters. Candidate C maybe recommended his/her supporters to explicitly reject A and B. As a result A and B will get more rejects (>50%) than C (<50%). Candidate C wins although he/she had less first preference support than A and B, it is not centrist (sincere Condorcet winner), most reject votes are strategic (not sincere), and C was the most strategic candidate.</div><div class=""><br class=""></div><div class="">The 25% prefer elimination limit is quite high. If there are no "near clones" that many voters prefer as equal best candidates, we may typically have max three candidates left after the disqualification round (unless all were disqualified and as a result none).</div><div class=""><br class=""></div><div class="">At least 20 of the A supporters and at least 20 of the B supporters reject other candidates (quite possible). Less than 50 of the A and B supporters (combined) reject C (quite possible). All C supporters reject other candidates (not probable but we could be quite close to that, and some additional rejects by A and B supporters would fill that gap). It seems that general rejection of competitors is a good strategy, and with three candidates of about equal strength, the number of strategic reject votes might easily determine the winner (instead of the number of positive sincere votes).</div><div class=""><br class=""></div><div class="">Any misses this time? :-)</div><div class=""><br class=""></div><div class="">BR, Juho</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Definition of PAR:</div><div class=""><div class=""><ol style="margin: 0.3em 0px 0px 3.2em; padding: 0px; color: rgb(37, 37, 37); font-family: sans-serif; font-size: 14px;" class=""><li style="margin-bottom: 0.1em;" class=""><b class="">Voters can Prefer, Accept, or Reject each candidate.</b> Default is "Reject" for voters who do not explicitly reject any candidates, and "Accept" otherwise.</li><li style="margin-bottom: 0.1em;" class=""><b class="">Candidates with a majority of Reject, or with under 25% Prefer, are disqualified</b>, unless that would disqualify all candidates.</li><li style="margin-bottom: 0.1em;" class="">Each voter gives 1 point to each non-eliminated candidate they prefer; and any voter who gave no such points (because their preferred candidates were all eliminated) gives 1 point to each non-eliminated candidate they accept. <b class="">The winner is the candidate with the most points.</b></li></ol></div></div><div class=""><br class=""></div><br class=""><div><blockquote type="cite" class=""><div class="">On 11 Nov 2016, at 18:28, Juho Laatu <<a href="mailto:juho.laatu@gmail.com" class="">juho.laatu@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html charset=us-ascii" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">Sorry, I missed the 25% preference rule. I'll think a bit more if there are still problems and good examples when the 25% preference rule is applied.</div><div class=""><br class=""></div><div class="">BR, Juho</div><div class=""><br class=""></div><br class=""><div class=""><blockquote type="cite" class=""><div class="">On 11 Nov 2016, at 18:17, Jameson Quinn <<a href="mailto:jameson.quinn@gmail.com" class="">jameson.quinn@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">In the case that Juho discusses, PAR is designed to disqualify/eliminate the minor candidates X, Y, Z, etc. due to the fact that they will have under 25% first preferences. The theory is that any candidate X with over 25% first preferences will be getting enough attention so that voters who don't like X, and who explicitly reject at least one candidate, will take the trouble to explicitly reject X. </div><div class="gmail_extra"><br class=""><div class="gmail_quote">2016-11-11 11:05 GMT-05:00 Juho Laatu <span dir="ltr" class=""><<a href="mailto:juho.laatu@gmail.com" target="_blank" class="">juho.laatu@gmail.com</a>></span>:<br class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class="">Negative votes and default votes that are not bottom votes are often problematic. There can be some problems also with rule "default is accept for voters who do explicitly reject some candidates".</div><div class=""><br class=""></div><div class="">Candidates A and B are considered to be the strongest potential winners. Their first preference support is about 45% and 45%. Candidates from C to Z have much less first preference support.</div><div class=""><br class=""></div><div class="">It makes sense to A supporters to reject B (hoping that rule 2 will eliminate B, even if B would have more support than A). B supporters will do the same to A. It is thus possible (or even probable in this scenario, if the election is competitive) that the leading candidates will be eliminated.</div><div class=""><br class=""></div><div class="">Let's assume that there are no obvious compromise candidates that would be preferred over B by A supporters, and vice versa. Some of the other (than A and B) candidates might be rejected too (those that many enough voters bother to reject sincerely). As a result the winner will be someone that could be quite disliked among both A and B supporters.</div><div class=""><br class=""></div><div class="">A linear opinion space might look like this: D - [C] - [A] - [B] - [E] - F - [G] - ... - X - Y - Z where square brackets point out the eliminated candidates. D and F are maybe the most likely winners, but surprises are possible if many A and B supporters explicitly reject (sincerely but incompletely) only few smaller candidates (e.g. D, C, E, F, G) and thereby give default accept to all the others (e.g. X, Y, Z). If candidate Y has more first preference support than other minor candidates, and some support from X and Z supporters, he/she might win.</div><div class=""><br class=""></div><div class="">If this is of concern, the easiest fix is of course to use reject as default value in all ballots.</div><div class=""><br class=""></div><div class="">BR, Juho</div><span class=""><div class=""><br class=""></div><br class=""><div class=""><blockquote type="cite" class=""><div class="">On 10 Nov 2016, at 17:39, Jameson Quinn <<a href="mailto:jameson.quinn@gmail.com" target="_blank" class="">jameson.quinn@gmail.com</a>> wrote:</div><br class="m_1169996365923893432Apple-interchange-newline"><div class=""><div dir="ltr" class=""><br class=""><div class="gmail_extra"><br class=""><div class="gmail_quote">2016-11-10 9:04 GMT-05:00 C.Benham <span dir="ltr" class=""><<a href="mailto:cbenham@adam.com.au" target="_blank" class="">cbenham@adam.com.au</a>></span>:<br class=""><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF" class="">
<div class="m_1169996365923893432gmail-m_-4276529064168255280moz-cite-prefix">
<blockquote type="cite" class="">1. Voters can Prefer, Accept, or Reject
each candidate. Default is Accept.</blockquote>
<br class="">
This seems to assume that all the voters are interested in all the
candidates and like checking boxes, whereas<br class="">
I should think that a lot of voters would be only interested in
their favourite and content to keep voting the<br class="">
way they did under plurality (and would presumably continue to do
so under Approval).<br class="">
<br class="">
They should be allowed to continue giving the most effective vote
possible by simply giving a "Prefer" rating to their<br class="">
favourite. In-effect penalising such voters for forgetting to
also give "Rejects" to all their non-favourites is unfair<br class="">
and dumb.<br class="">
<br class="">
It will give voters who aren't fans of the new method extra reason
to resent it. Suppose that a strong candidate<br class="">
from an established party very narrowly loses just because some of
his/her supporters forgot to give out "Rejects".<br class="">
Don't you think that might fuel a movement to dump the method?<br class=""></div></div></blockquote><div class=""><br class=""></div><div class="">My thinking was that in most real-world situations, you'd only have to check one prefer and one reject to get maximum effectiveness, and it would be obvious which to reject.</div><div class=""><br class=""></div></div></div></div></div></blockquote><blockquote type="cite" class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class="">But I see your point. So I'm changing the method to: "Default is reject for voters who do not explicitly reject any candidates, or accept for those who do." <br class=""></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div bgcolor="#FFFFFF" class=""><div class="m_1169996365923893432gmail-m_-4276529064168255280moz-cite-prefix"><br class=""><blockquote type="cite" class="">2.Candidates with a majority of Reject, or with under 25% Prefer, are eliminated, unless that would eliminate all candidates.</blockquote><div class=""><br class=""></div></div></div></blockquote></div></div></div></blockquote><div class=""><br class=""></div></div><br class=""></span></div><br class="">----<br class="">
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