Benjamin:<div><br></div><div>You are right to point out that we should have some discussion of basic principles to underly our discussion of specific systems. Here are my own views:</div><div><br></div><div>1. There is no single easy philosophical answer to these questions. There will always be those who, like Clay, would rather grab the quick self-consistent certainty of interpersonally-summable utilities; and it is true that this point of view offers many advantages (for instance, immediate immunity to probabilistic or Arrovian money-pump arguments); but it also has serious philosophical critiques. There is a continuum of possible self-consistent answers to the breadth-versus-depth question that runs from maximin to summed-utility to maximax, and if you allow certain kinds of status-quo bias, the possibilities are even broader.</div>
<div><br></div><div>2. However, for practical terms, we are not likely to get a better metric for voting systems than total utility. A maximin metric would philosophically give veto power to a single voter; an intermediate metric would probably be equivalent to summed-utility if you rescale utility by some monotic function; and any metric involving status quo bias extrinsic to the voters themselves, is a horrible compass for system design. So while I don't share Clay's easy certainty about the impeccable solidity of the philosophical foundations here, I do agree with him that this is the best single measure of outcome quality.</div>
<div><br></div><div>3. That doesn't make things easy, though. For instance, for a given set of ballots, the Score result is usually (though not always!) the best way to use the information given to try to maximize the underlying utilities. But since voters will almost certainly vote differently under different systems, that does not mean that Score is the best way to ensure the best result from a pre-balloting point of view. Or another instance: system A could give better results, but system B might be more likely to be implemented and thus offer more expected value over status quo C.</div>
<div><br></div><div>Jameson</div><div><br><div class="gmail_quote">2013/6/30 Benjamin Grant <span dir="ltr"><<a href="mailto:benn@4efix.com" target="_blank">benn@4efix.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div lang="EN-US" link="#0563C1" vlink="#954F72"><div><p>I’ve been coming at understanding better the options and choices, merits and flaws of various approaches to holding votes – mostly with the kind (and sometimes not-so-kind) help of the people on this list.<u></u><u></u></p>
<p><u></u> <u></u></p><p>However, a (I assume) basic thought occurred to me, which may be so obvious no one need ever discuss it, but I want to double check my thinking on some of this.<u></u><u></u></p><p><u></u> <u></u></p>
<p>The rest of this post will NOT be concerned with any one particular voting method or criteria. Instead I will be comparing different scenarios of voter preference with thoughts about who “should” win. If I am not making sense quite yet, come along and hopefully it will make more sense in practice. If not, you can ask me questions or delete the post.<u></u><u></u></p>
<p><u></u> <u></u></p><p>Let’s assume that we have a magical gift – a super power, if you will. We can know exactly what each voter thinks about each candidate. Now, because this comes from magic, it cannot unfortunately be used as a part of the election process, but it will be useful for our examination of attitudes of the voters.<u></u><u></u></p>
<p><u></u> <u></u></p><p>So as we turn our power on a random voter, we can pick (on a scale of 0 to 100) how they feel about each candidate. A 0, in this case, indicates that the voter is absolutely against the candidate winning the election, and will vote however he must to stop that from happening, whereas a 100 indicates the reverse: that the voter is absolutely for this candidate’s victory, and will give it everything he can at the ballot box. 50 indicates a sort of “meh” reaction – doesn’t hate them, doesn’t love them – or possibly the voter has some aspects of the candidate he really likes, but some other aspects that he is less than thrilled with.<u></u><u></u></p>
<p><u></u> <u></u></p><p>So, using this power, we can know absolutely on a scale of 0 to 100 what each voter thinks of each candidate. Using that knowledge, we ought to be able to say who “should” win – which I will return to in just a moment.<u></u><u></u></p>
<p><u></u> <u></u></p><p>First, each candidate’s support by the voters can be noted on a graph, with the X axis denoting the scale of 0-100 Favorability, and the Y axis denoting the percentage of voters who hold that exact opinion.<u></u><u></u></p>
<p><u></u> <u></u></p><p>So, for example, on a graph like this, you might find that 12% rate a certain candidate at 0F – they *hate* this guy. Another 14% may rate this candidate at 100F – these are his loyal base. Most people fall somewhere in between.<u></u><u></u></p>
<p><u></u> <u></u></p><p>To keep things simple, I’m going to talk about candidates as if their voters clump at certain points, instead of spreading more fuzzily. I think the core questions become no less valid and no less worth thought.<u></u><u></u></p>
<p><u></u> <u></u></p><p>I am going to posit a series of two candidate comparisons, and ask who “should” win. The point here is to ignore the methods for a bit, and just see what our gut says, given the absolutely magically accurate information we have about the voter’s preferences.<u></u><u></u></p>
<p><u></u> <u></u></p><p>To start with, let’s imagine one candidate with 51% of the voters giving him an 80F, and 49% giving him a 0F. Another candidate has a 63% of the voters giving an 80F (with the remaining 37% giving 0F.) Which candidate ought to win?<u></u><u></u></p>
<p><u></u> <u></u></p><p>Unless I miss something, this one is an easy one. Both candidates have the same level of favorability but one has greater breadth than the other. It seems self-evident to say that when the favorability is identical, but the breadth is not, greater breadth should win.<u></u><u></u></p>
<p><u></u> <u></u></p><p>Likewise, if instead our election has one fellow with 51% @ 80F and another at 51% @ 100F, the second ought to win, since he has the same breadth, but higher favorability, right?<u></u><u></u></p>
<p><u></u> <u></u></p><p>(Note, if I say that a candidate has 51% @ 80F, not only does that mean 51% of the voters find him at an 80 Favorability, but that all other voters omitted (the 49%) find him at 0F. Additionally please note that these are NOT elections or election methods, just questions about who we feel “should” win given different circumstances of voter sentiment.)<u></u><u></u></p>
<p><u></u> <u></u></p><p>So, when one candidate has equal or better breadth and/or favorability, it makes sense to our sense of fairness that they ought to win. Now let’s examine the more complex and fun situation of unequal aspects – with one candidate with a better breadth, but his competitor with a better favorability.<u></u><u></u></p>
<p><u></u> <u></u></p><p>This time, we have a candidate named Wilson who manages to get 51% @ 100F. His competitor Franklin gets 80% @ 90F.<u></u><u></u></p><p><u></u> <u></u></p><p>In this circumstance, I think a lot of us would prefer that Franklin win. Sure, 51% of the voters like Wilson better than Franklin, but at least 29% of them (and possibly more) still like Franklin almost as much – and only 20% of the voters don’t like Franklin. Franklin is, I think, the ideal example of a compromise candidate – he not the first choice of the majority, but he is well chosen by a broad swath.<u></u><u></u></p>
<p><u></u> <u></u></p><p>Now let’s change that up. Let’s say that it’s four years later, and people’s opinions have changed. Wilson still gets 51% @ 100F, but now Franklin gets 80% @ 52F. The bloom is off Franklin’s rose.<u></u><u></u></p>
<p><u></u> <u></u></p><p>At this point, Franklin is looking less like a comprise candidate that everyone can get behind, and more like a bland fellow that 80% don’t hate, but don’t like all that much either. Given how strongly Wilson’s 51% feel, I think it’s natural to think that in this election, Wilson ought to win – his breadth is narrower, but the favorability he has is unmatched by Franklin’s lukewarm support, which is barely above a mediocre average(52F).<u></u><u></u></p>
<p><u></u> <u></u></p><p>This brings me to my main thought. As we compare candidates using perfect knowledge of how the voters favor them (or disfavor them), at what point does our guts, intuition, and instinct for fairness cause us to flip our support from one candidate to another? Are our transition points naturally similar, or fundamentally different, based on perhaps a different valuing of compromise or partisanship?<u></u><u></u></p>
<p><u></u> <u></u></p><p>Here’s one more example. Using our voter detection superpowers on yet another election, we find Wilson to be steady at 51% @ 100F, 10% @ 50F, and 39% @ 0F. Franklin is now at 10% @ 85F, 55% @ 75F, and 35% @ 50F.<u></u><u></u></p>
<p><u></u> <u></u></p><p>Who ought to win? Screw (for now) the conversation of what method to use and what criteria it serves or breaks. In our hearts, should Wilson or Franklin win? Wilson has over half of the voters at *maximum* favorability, while Franklin’s bulk is only at between 75F and 85F – but on the other hand, Wilson has almost 40% of the voters hating him, while the *lowest* rank Franklin got was only by 35% of the voters, and was a full 50F, meaning that even the least favorable people for Franklin thought he was “alright”.<u></u><u></u></p>
<p><u></u> <u></u></p><p>So, which is the right choice, the loved and hated Wilson, or the generally somewhat respected but neither loved or hated Franklin? <u></u><u></u></p><p><u></u> <u></u></p><p>If you found this easy to answer, then slide the numbers a little in the other direction (disfavoring slightly more your easy choice) – you will find a point of transition where it become almost impossible to say with honesty that one deserves the victory more than the other. This is your personal “fairness threshold”.<u></u><u></u></p>
<p><u></u> <u></u></p><p>It seems to me that while it is important to figure out voting methods that fail less often (and less spectacularly), it is also important to figure out what kind of results in these basic circumstances we are looking for. Instead of just focusing on how and why voting methods become broken or dysfunctional, perhaps it would be a good idea beforehand to try to figure out our “design spec” or goals for the system to begin with. Apart from some of the weird behavior, apart from the pull between strategic and sincere voting, what are the fairness thresholds we want in a voting system? At what point do we want breadth to defeat favorability, or vice versa? It seems that this is a question we can answer utterly independently of any system concerns, and it’s only after answering this question that we can use this as *another* metric of the desirability of any particular voting system.<u></u><u></u></p>
<p><u></u> <u></u></p><p>After all, if a voting method fails to give us winners at thresholds we consider fair, then the rest of it doesn’t much matter, right?<u></u><u></u></p><p><u></u> <u></u></p><p>So I will finish with an uncertainty: do these thresholds, the points at which shifting one way in favorability or breadth or both makes A win, shift the other way, B wins – are these points more or less similar for all of us, or is it true that there is widespread disagreement on the matter? For example, with Wilson getting 51% @ 100F and Franklin getting 80% @ 90F, are there many who think Wilson should still win? <u></u><u></u></p>
<p><u></u> <u></u></p><p>Or alternatively, with Wilson getting 51% @ 100F and Franklin getting 80% @ 52F, are there many who think Franklin should win? <u></u><u></u></p><p><u></u> <u></u></p><p>Or do we all not perhaps have the *exact* same “fairness thresholds”, *but* pretty close, in the same neighborhood?<u></u><u></u></p>
<p><u></u> <u></u></p><p>If we have utterly unrelated fairness thresholds, then we ought to probably acknowledge the fairness threshold built into our choices of voting methods. So if Ted always values breadth over favorability, and I always do the reverse, then we ought not to have an expectation of the voting systems Ted favors to have much if any overlap with the ones that I do.<u></u><u></u></p>
<p><u></u> <u></u></p><p>On the other hand, if the “fairness threshold” for most people is in the same neighborhood, then perhaps it might make sense to determine what it is a little more precisely, so that we can use it as another more positive standard for the systems that are invented and discussed.<u></u><u></u></p>
<p><u></u> <u></u></p><p>What do you think?<u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><span style="color:#1f497d">-Benn Grant<u></u><u></u></span></p><p class="MsoNormal"><span style="color:#1f497d">eFix Computer Consulting<u></u><u></u></span></p>
<p class="MsoNormal"><span style="color:#1f497d"><a href="mailto:benn@4efix.com" target="_blank"><span style="color:#0563c1">benn@4efix.com</span></a><u></u><u></u></span></p><p class="MsoNormal"><span style="color:#1f497d">603.283.6601<span class="HOEnZb"><font color="#888888"><u></u><u></u></font></span></span></p>
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