<div dir="ltr"><div><div>I agree with all of your comments, but my new definition of Most Approved Immune overcomes our common objection to the old definition (it sounds baad to start from the bottom).<br><br></div>And I like your new Score based method of gradual collapse of pairwise preferences in order of increasing magnitudes of score differences. <br><br>It reminds me of one of our dyadic approval variants where we removed rank relations in order of increasing strength, i.e. first all single chevron relations >, then all doubles >>, then all triples >>>, etc. until only the strongest relation remained >>>...>>> (if necessary). The dyadic condition was that these relations could be encoded with scores in binary so that the successive collapses could be accomplished by erasing least significant binary digits.<br><br></div>I wonder if there is any chance that it satisfies the FBC.<br><div><div><div><div class="gmail_extra"><div class="gmail_quote"><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Date: Fri, 18 Nov 2016 00:35:24 +1030<br>
From: "C.Benham" <<a href="mailto:cbenham@adam.com.au">cbenham@adam.com.au</a>><br>
To: Forest Simmons <<a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</a>>, Michael Ossipoff<br>
<<a href="mailto:email9648742@gmail.com">email9648742@gmail.com</a>><br>
Cc: EM <<a href="mailto:election-methods@lists.electorama.com">election-methods@lists.<wbr>electorama.com</a>><br>
Subject: Re: [EM] Trying to have CD, protect strong top-set, and<br>
protect middle candidates too<br>
Message-ID: <<a href="mailto:09ddf69f-495a-5f7c-42ac-24063d2e570c@adam.com.au">09ddf69f-495a-5f7c-42ac-<wbr>24063d2e570c@adam.com.au</a>><br>
Content-Type: text/plain; charset="utf-8"; Format="flowed"<br>
<br>
On 11/17/2016 9:00 AM, Forest Simmons wrote:<br>
<br>
> Here's a simple method that is essentially Smith//Approval without<br>
> having to mention the Smith set:<br>
><br>
> List the candidates in order of approval, highest to lowest, top to<br>
> bottom. While any candidate pairwise beats an adjacent candidate<br>
> higher in the list, switch places of the two lowest out of order<br>
> adjacent members.<br>
><br>
> When there remains no out of order adjacent pair, elect the candidate<br>
> at the top of the list.<br>
<br>
Forest,<br>
<br>
I like Smith//Approval and your usually equivalent Max Covered Approval<br>
method.<br>
<br>
But in this version, the stipulation that we "switch places of the two<br>
/lowest/ out of order adjacent members" could look a bit arbitrary and<br>
less smooth<br>
than Margins-Sorted Approval.<br>
<br>
BTW, it seems to me that both this and Smith//Approval can handle the<br>
Chicken Dilemma situation quite well if we use ranked ballots with<br>
approval cut-offs.<br>
<br>
(Or ratings ballots with many slots that register approval and as many<br>
(or maybe as few as only 2) that register unapproval.)<br>
<br>
<a href="http://wiki.electorama.com/wiki/Approval_Sorted_Margins" rel="noreferrer" target="_blank">http://wiki.electorama.com/<wbr>wiki/Approval_Sorted_Margins</a><br>
<br>
<a href="http://wiki.electorama.com/wiki/Approval_Cutoff" rel="noreferrer" target="_blank">http://wiki.electorama.com/<wbr>wiki/Approval_Cutoff</a><br>
<br>
And here's another smooth Condorcet method that should do as well:<br>
<br>
*Voters score the candidates on some scale that allows large and varied<br>
gaps between the candidates: say 0-100.<br>
Elect the CW if there is one.<br>
<br>
Otherwise compress the 1-point gaps (if any) on all ballots into<br>
zero-point gaps (so that those ballots abandon their original pairwise<br>
preference for any<br>
X originally scored only one point more than any Y).<br>
<br>
Based on the thus modified ballot information, elect the CW if there is one.<br>
<br>
Otherwise compress the 2-point gaps (if any) on all ballots into<br>
zero-point gaps (so that those ballots abandon their original pairwise<br>
preference for any<br>
X originally scored two points more than any Y).<br>
<br>
Based on the thus modified ballot information, elect the CW if there is one.<br>
<br>
And so on, as gradually as possible compressing larger and larger gaps<br>
until we have a pairwise beats-all winner.*<br>
<br>
Chris Benham<br>
<br>
<br>
On 11/17/2016 9:00 AM, Forest Simmons wrote:<br>
> Here's a simple method that is essentially Smith//Approval without<br>
> having to mention the Smith set:<br>
><br>
> List the candidates in order of approval, highest to lowest, top to<br>
> bottom. While any candidate pairwise beats an adjacent candidate<br>
> higher in the list, switch places of the two lowest out of order<br>
> adjacent members.<br>
><br>
> When there remains no out of order adjacent pair, elect the candidate<br>
> at the top of the list.<br>
><br>
> Note that the winner will automatically be a member of the top cycle,<br>
> and if it is a cycle of three, it will be the most approved member of<br>
> the cycle.<br>
><br>
> Also notice that it yields an unambiguous social order, and that there<br>
> can be no second place complaint.<br>
><br>
><br>
><br>
><br>
><br>
> On Tue, Nov 15, 2016 at 5:19 PM, Michael Ossipoff<br>
> <<a href="mailto:email9648742@gmail.com">email9648742@gmail.com</a> <mailto:<a href="mailto:email9648742@gmail.com">email9648742@gmail.com</a><wbr>>> wrote:<br>
><br>
> When I started my current EM participation, I was saying that<br>
> 3-Slot ICT was my favorite method.<br>
><br>
> That doesn't conflict with saying that I consider Approval the<br>
> best, because I regard 3-Slot ICT, or unlimited-rankings ICT (when<br>
> used approval-like) as an Approval version without chicken-dilemma.<br>
><br>
> Later I realized that MDDTR is better than ICT, because it gives<br>
> better protection to middle candidates.<br>
><br>
> I measure that protection by how well they'd be protected if they<br>
> were CWs. ...what it would take to protect their win, and how<br>
> well it's protected.<br>
><br>
> I define "middle candidates" as candidates you rank or rate below<br>
> top and above bottom.<br>
><br>
> ICT gives no protection to middle candidates, against burial, or<br>
> even against innocent, non-strategic truncation--the two things<br>
> that threaten a CWs in pairwise-c0unt methods.<br>
><br>
> MDDTR gives full truncation-proofness to middle candidates, but<br>
> (contrary to what I earlier believed), its protection of middle<br>
> candidates against burial can only be called "shabby".<br>
><br>
> By the way, I no longer think that ICT or MDDTR needs to be<br>
> 3-slot. 3-Slot would be fine with me, because I believe that ICT<br>
> or MDDTR should be used as Approval, and that middle rating or<br>
> ranking should only be used when seriously needed to deter<br>
> chicken-dilemma defection. When middle is used in an<br>
> unlimited-ranking MDDTR or ICT, it should probably consist of<br>
> 2nd-place ranking, if you want to give the demoted candidates the<br>
> best protection. ...but maybe you'd rather rank them with<br>
> respect to eachother, at different middle levels, as I probably<br>
> sometimes would.<br>
><br>
> But, as I've been saying, activists & organizations seem to like<br>
> rankings, and some people--overcompromisers & rival parties--might<br>
> very well need rankings to soften their voting errors.<br>
><br>
> And it seems to me that there's no particular reason not to rank,<br>
> in order of preference, your middle candidates, if some of them<br>
> are better than others, or if the voters of some of them are less<br>
> trustworthy than others.<br>
><br>
> So, that's if you want CD, in addition to FBC, and good protection<br>
> for middle candidates<br>
><br>
> Even if you're using the method as Approval, you still want your<br>
> demoted candidate(s) to be well protected. Just because you don't<br>
> trust hir voters doesn't mean you want to throw her to the hounds<br>
> and thereby lower Pt, the probability of electing from your strong<br>
> top-set.<br>
><br>
> Anyway, so far, this is all referring to CD methods.<br>
><br>
> Of those, I like MDDTR best. As a rank method, it (as i said)<br>
> gives only shabby burial-protection to a middle candidate. But<br>
> evidently (please tell me it isn't so) you can't have FBC, CD, and<br>
> good protection of middle candidates.<br>
><br>
> I consider CD more important to how well protected middle<br>
> candidates are. Yes, FBC + CD give poor protection to middle<br>
> candidates, and that lessens the value of their CD. But non-CD<br>
> methods don't have CD at all, and that's worse.<br>
><br>
> So I prefer MDDTR to methods that give better protection to middle<br>
> candidates, but don't have CD.<br>
><br>
> So, where I used to say that my favorite method is 3-Slot ICT, now<br>
> I say that my favorite method is MDDTR. Preferably with unlimited<br>
> rankings. (Though one could use only the 1st, 2nd, & bottom<br>
> positions if one chose to). ...regardable as a<br>
> chicken-dilemma-free version of Approval.<br>
><br>
> ------------------------------<wbr>------------------------------<wbr>------<br>
><br>
> Non-CD methods with better "middle-strategy" than CD methods:<br>
><br>
> But, in an election, I'm just one voter, and so, how well-suited<br>
> the method is to me is less important, and won't affect the<br>
> outcome as much, in comparison to how well-suited the method is to<br>
> lots of progressives.<br>
><br>
> So, what if most progressives would rather have a method that's<br>
> really good as a rank method, a method that has good "middle<br>
> strategy" (strategy for protecting a middle candidate's win if<br>
> s/he's CWs).<br>
><br>
> That would be important if you knew that all or nearly all, or<br>
> even most of them were going to use the method purely as a rank<br>
> method.<br>
><br>
> Bucklin is the traditional FBC rankings-method.<br>
><br>
> I distinguish 2 kinds of middle strategy merit:<br>
><br>
> 1. How well the method protects top-ranked candidates against<br>
> middle-ranked candidates. I call that "Middle1"<br>
><br>
> 2. How well the lmethod protects a middle-ranked candidate<br>
> against any candidate you rank lower than hir. I call that "Middle2".<br>
><br>
> So, how to get the best middle strategy, with the main goal still<br>
> being keeping a good probability, Pt, of electing from your strong<br>
> top-set?<br>
><br>
> MDDTR's middle1 seems better than that of Bucklin. In MDDTR,<br>
> you're voting to contribute to a majority for your top against<br>
> your middle. In Bucklin, you can protect top against middle by<br>
> skipping some rating-levels above the middle candidates. In that<br>
> way, you can give the top candidates time to receive the<br>
> coalescing lower-choice votes that they'll get from the preferrers<br>
> of other candidates, before giving anything to the middle candidates.<br>
><br>
> That's a bit more work than just ranking in order of preference.<br>
> It requires you to judge where, and how far down in rankings, your<br>
> top candidates are going to receive lower-choice votes from.<br>
><br>
> So I suggest that MDDTR does better at Middle1 than Bucklin does.<br>
><br>
> But Bucklin does better at Middle2.<br>
><br>
> In Bucklin, the CWs's win is protected by the people who<br>
> pretty-much agree with you, the people of your wing, merely not<br>
> ranking down too far.<br>
><br>
> MDDTR needs that too, but it isn't enough to give MDDTR more than<br>
> shabby protection.<br>
><br>
> ...And Bucklin's Middle1, though not as convenient or easy as that<br>
> of MDDTR, isn't as questionable as MDDTR's Middle2.<br>
><br>
> So, overall, I'd say that Bucklin's Middle Strategy is better than<br>
> that of MDDTR. So, for people who want to use the method purely as<br>
> a rank-method, Bucklin is better than MDDTR.<br>
><br>
> Bucklin also has the advantage of use-precedent. MDDT has the<br>
> advantage of precinct-summability,but I don't consider that<br>
> essential.<br>
><br>
> For voters using the method purely as a rank method, I'd prefer<br>
> Bucklin to MDDTR.<br>
><br>
> Chicken dilemma won't happen all the time, probably won't happen<br>
> often. But middle-protection will always matter to people using it<br>
> as a rank method.<br>
><br>
> But it seems to me that, once we give up CD (for voters who need<br>
> good middle strategly, because of their rank voting), then it<br>
> might be possible to do better than Bucklin.<br>
><br>
> It seems to me that methods that use both Approval and<br>
> pairwise-count can do better than Bucklin, at middle protection.<br>
><br>
> A lot of methods of that kind have been proposed, and I've ignored<br>
> all of them because they don't meet CD. But, as mentioned above,<br>
> for some electorates, middle strategy could be more important.<br>
><br>
> It seems to me that MDDA (also evidently named MPOA) and<br>
> Smith//Approval are two methods that might be better than Bucklin<br>
> at middle protection..<br>
><br>
> Using Approval as the cycle-solution is a very powerful idea (if<br>
> you're willing to give up CD, for an electorate's needs). But most<br>
> of you already knew that, before I paid attention to it<br>
> (...because I was only looking at CD methods)..<br>
><br>
> MDDA's & Smith//Approval's burial vulnerability doesn't matter<br>
> much, when the Approval winner wins the cycle. In fact,<br>
> Smith//Approval's truncation-vulnerability could even be regarded<br>
> as an advantage, for when your strong top-set doesn't include the CWs.<br>
><br>
> MDDA & Smith//Approval look better to me than Bucklin.<br>
><br>
> Simpler Middle1.<br>
><br>
> Precinct-Summability is an added bonus.<br>
><br>
> MDDA seems to have a briefer definition than either Bucklin or<br>
> Smith//Approval, and brief definition can be decisive.<br>
><br>
> I know of Bucklin being rejected when MDDTR was accepted. MDDA<br>
> would almost surely have been accepted too.<br>
><br>
> I don't think Smith//Approval would go over well, with its need<br>
> to define the Smith set, which greatly lengthens the definition.<br>
><br>
> For an electorate that need good Middle1 & Middle2 more than CD,<br>
> MDDA seems the winner so far.<br>
><br>
> Smith//Approvsl of course meets Smith. ...which of course means<br>
> that it fails FBC. But does it need FBC?<br>
><br>
> It could be argued (but I don't know if it's true) that<br>
> Smith//Approval doesn't need FBC, because, though you don't have<br>
> an efffective Approval vote at the top, you still can vote<br>
> Approval, with the approval-cutoff, or by only ranking your strong<br>
> top-set.<br>
><br>
> So, though Compromise could become pair-beaten by Favorite because<br>
> you raise Favorite to top with Compromise, resulting in a cycle<br>
> instead of a CWv win for Favorite, the cycle will be judged by<br>
> approvals, and you're approved only your strong top-set.<br>
><br>
> Of course, just because Favorite was almost the CWv doesn't<br>
> necessarily mean that s/he'll win the Approval count. But are you<br>
> any worse off than you'd have been with MDDA?<br>
><br>
> Forest (but maybe others too) has proposed a number of methods<br>
> that combine pairwise-count and Approval. Do any of those beat<br>
> MDDA & Smith//Approval by the standards of protecting one's strong<br>
> top-set, and Middle1 & Middle2?<br>
><br>
> in particular, do any of them do better than MDDA by those<br>
> standards? Do any do as well as MDDA by those standards and have<br>
> as brief a defintion, or nearly as brief a definition?<br>
><br>
> In other words, are there methods that achieve those things better<br>
> than MDDA & Smith//Approval, or achieve them better than MDDA and<br>
> have as brief a definition?<br>
><br>
> In fact, is there a method that meets FBC (or doesn't need it),<br>
> meets CD, and does as well by Middle1 & Middle2 as MDDA,<br>
> Smith//Approval or Bucklin?<br>
><br>
> Michael Ossipoff<br>
><br>
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</blockquote></div><br></div></div></div></div></div>