<div dir="ltr">The first round of Step 3 could be made summable with the addition of an NxN array where row i accumulates, from a ballot that does not Prefer the i-th candidate, Accept points cast for any candidates besides the i-th candidate.<div><br></div><div>I'm not sure if that same array could be used for step 4, however. In fact, step 4 is not entirely clear to me.<br><div><br></div><div>Ted</div></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Mon, Nov 14, 2016 at 10:14 AM, Jameson Quinn <span dir="ltr"><<a href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">I'm still working on getting PAR expressed in the best format. Here's the latest:<div><br></div><div><ol style="margin:0.3em 0px 0px 3.2em;padding:0px;color:rgb(37,37,37);font-family:sans-serif;font-size:14px"><li style="margin-bottom:0.1em"><b>Voters Prefer, Accept, or Reject each candidate.</b> On ballots which don't explicitly use "Reject", or for candidates with less than 25% "Prefer", blanks count as "Reject"; otherwise, blanks count as "Accept".</li><li style="margin-bottom:0.1em"><b>Tally 1 point for each "Prefer"</b> for each candidate.</li><li style="margin-bottom:0.1em">Out of the candidates (if any) with no more than 50% "Reject", find the one with the most points. <b>For every ballot which doesn't "Prefer" this frontrunner, add 1 point for each "Accept".</b></li><li style="margin-bottom:0.1em">If the frontrunner changed, add 1 for each "Accept" that's not yet tallied (the ones which "Prefer" the original frontrunner). <b>Most points wins.</b></li></ol><div><font color="#252525" face="sans-serif"><span style="font-size:14px"><b><br></b></span></font></div></div><div><font color="#252525" face="sans-serif"><span style="font-size:14px">I now believe that the system as expressed above meets the voted majority Condorcet criterion. Which means that FBPPAR (almost) meets both FBC and voted majority Condorcet! Impossible, you say? No; approval meets both of these criteria (because it reduces "voted Condorcet" to a triviality), and FBPPAR reduces to approval when voters strategize expecting a Condorcet cycle.</span></font></div><div><span style="font-size:14px;color:rgb(37,37,37);font-family:sans-serif"><br></span></div><div><span style="font-size:14px;color:rgb(37,37,37);font-family:sans-serif">What do I mean by "(almost)" above? Well, FBPPAR allows voters to rate a candidate as "prefer, but do not make them frontrunner because of my vote". This is useful for cyclical and near-cyclical situations (that is, for A>B voters who know that most B votes are B>C and that C beats A). But if this option is used in cases where it is not actually strategic, it breaks the voted majority Condorcet property. </span><br></div><div><font color="#252525" face="sans-serif"><span style="font-size:14px"><br></span></font></div><div><font color="#252525" face="sans-serif"><span style="font-size:14px">So FBPPAR is a system that meets FBC; deals with center squeeze via a fairly strong Condorcet-like property; deals with chicken dilemma without a slippery slope; can be counted in at most 3 rounds, each of which is O(N) summable; meets majority and mutual majority; meets a weakened version of later-no-help; outputs tallies that are summable with other approval tallies; and is basically all-around awesome. Personally, I feel that FBPPAR essentially dominates other 3-rank systems in terms of strategic properties; and that PAR is, in the real world, a very close approximation of FBPPAR that's justified by its greater simplicity.</span></font></div></div><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">2016-11-13 18:04 GMT-05:00 Jameson Quinn <span dir="ltr"><<a href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><p style="margin:0.5em 0px;line-height:inherit;color:rgb(37,37,37);font-family:sans-serif;font-size:14px">Yet another revision of the rules. This one fixes it so that, if no candidates pass both thresholds, "accept" votes count.</p><span><p style="margin:0.5em 0px;line-height:inherit;color:rgb(37,37,37);font-family:sans-serif;font-size:14px"><br></p><p style="margin:0.5em 0px;line-height:inherit;color:rgb(37,37,37);font-family:sans-serif;font-size:14px">Prefer Accept Reject (PAR) voting works as follows:</p></span><ol style="margin:0.3em 0px 0px 3.2em;padding:0px;color:rgb(37,37,37);font-family:sans-serif;font-size:14px"><li style="margin-bottom:0.1em"><b>Voters Prefer, Accept, or Reject each candidate.</b> On ballots which don't explicitly use "Reject", blanks count as "Reject"; otherwise, blanks count as "Accept".</li><li style="margin-bottom:0.1em"><b>Of the candidates that are both "viable"</b> (at least 25% Prefer) <b>and "acceptable"</b> (no more than 50% reject), <b>the one with most "Prefer"s is called the leader.</b></li><li style="margin-bottom:0.1em">Each "Prefer" is worth 1 point. For viable candidates, each "Accept" on a ballot which doesn't prefer the leader is also worth 1 point. <b>Most points wins.</b></li></ol><div><font color="#252525" face="sans-serif"><span style="font-size:14px"><b><br></b></span></font></div><div><font color="#252525" face="sans-serif"><span style="font-size:14px">If I could do it without it sounding too complicated, I'd make it so that explicit "accept" votes can count for non-viable candidates. But I don't think it's worth even the minor extra complication it would take to explain that. </span></font></div><div><br></div><div>Note that changing the above system so that it passes FBC requires only giving a "prefer for the purposes of step 3, but count step 2 as if I rejected" option.</div><div><br></div><div>I think this system is pretty great in outcomes; and that, while it's certainly not the simplest method, it's not too complex.</div></div><div class="m_8017742133112175629HOEnZb"><div class="m_8017742133112175629h5"><div class="gmail_extra"><br><div class="gmail_quote">2016-11-12 23:33 GMT-05:00 Jameson Quinn <span dir="ltr"><<a href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><br><div class="gmail_extra"><br><div class="gmail_quote"><span>2016-11-12 17:45 GMT-05:00 Neal McBurnett <span dir="ltr"><<a href="mailto:nealmcb@gmail.com" target="_blank">nealmcb@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">I haven't been paying that much attention. But this definition doesn't define what this means "a rival is explicitly rejected". Is "rejected" the opposite of "viable"? Or does it mean that no other voter cast any "reject" vote for any other candidate? Or ???<br></blockquote><div><br></div></span><div>If candidates are ABCD, a ballot that prefers A and leaves the rest blank counts as rejecting BCD, but one that prefers A and rejects B and leaves the rest blank counts as accepting CD.</div><div><div class="m_8017742133112175629m_-4283512402372238459h5"><div><br></div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
So if I have an "accept" on a ballot that doesn't "prefer" the leader, that means 0 points?<br>
Since votes depend on how other votes are interpreted and who the leader is, is the tally guaranteed to be attracted to a single stable equilibrium tally?<br>
<br>
Thanks,<br>
<br>
-Neal<br>
<span><br>
On Sat, Nov 12, 2016 at 05:27:53PM -0500, Jameson Quinn wrote:<br>
> I think this is the best phrasing I've come up with so far for PAR. I think it's not exactly equivalent to the definitions I've<br>
> given before, but it is close enough to meet all the same properties and give the same result in any basic scenario type.<br>
><br>
> Prefer Accept Reject (PAR) voting works as follows:<br>
><br>
</span>> 1. Voters can Prefer, Accept, or Reject each candidate. Blanks count as "Reject" if no rival is explicitly rejected; otherwise,<br>
> blank is "Accept".<br>
> 2. Candidates with at least 25% Prefer, and no more than 50% reject, are "viable". The most-preferred viable candidate (if any) is<br>
> the leader.<br>
> 3. Each "prefer" is worth 1 point. For viable candidates, each "accept" on a ballot which doesn't prefer the leader is also worth<br>
<span>> 1 point. Most points wins.<br>
><br>
><br>
> 2016-11-12 13:47 GMT-05:00 Jameson Quinn <<a href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>>:<br>
><br>
> Thinking about PAR and the electoral college, I realized that there is a different way to state the PAR rules:<br>
><br>
</span>> 1. Voters can Prefer, Accept, or Reject each candidate. Default is "Reject" for voters who do not explicitly reject any<br>
> candidates, and "Accept" otherwise.<br>
> 2. A candidate is "viable" if they are rejected by under 50%.<br>
> 3. Each ballot gives 1 point to each candidate it prefers. Ballots which prefer no viable candidates also give 1 point to each<br>
<span>> candidate they accept, so long as that candidate is preferred by at least 25%.<br>
</span>> 4. Now find the viable candidate with the most points, if any, and redo step 3 from scratch as if only that candidate were<br>
> viable.<br>
> 5. The winner is the candidate with the most points.<br>
<div class="m_8017742133112175629m_-4283512402372238459m_-1235312590517853628HOEnZb"><div class="m_8017742133112175629m_-4283512402372238459m_-1235312590517853628h5">><br>
> This could potentially differ from PAR in that it waits slightly longer to "reveal" the preferences of candidates with under<br>
> 25% preferences. In practice, I doubt this would typically make any difference.<br>
><br>
> The procedure above is more complicated than PAR's, but the advantage is that it produces counts which include the disqualified<br>
> candidates, and thus is suitable for combining with totals from non-PAR systems such as approval, plurality, or<br>
> "pre-elimination totals" from IRV. <br>
><br>
><br>
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