<html><head><meta http-equiv="Content-Type" content="text/html charset=iso-8859-1"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;">On 11.1.2014, at 16.53, Michael Ossipoff <<a href="mailto:email9648742@gmail.com">email9648742@gmail.com</a>> wrote:<br><div><br class="Apple-interchange-newline"><blockquote type="cite"><div dir="ltr"><div class="gmail_extra"><div class="gmail_quote"><blockquote style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left-color: rgb(204, 204, 204); border-left-width: 1px; border-left-style: solid; position: static; z-index: auto;" class="gmail_quote">
<div class="im"><br>
> One voter definition of voting X over Y:<br>
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> A voter votes X over Y if s/he votes in such a way that, if X and Y were the only candidates, and if s/he were the only voter, and if the voting system is the one in which s/he is voting, then X would be the unique winner.<br>
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> [end of 1-voter definition of voting X over Y]<br>
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> That's what I mean by "voting X over Y"<br></div></blockquote><div> </div><div>You wrote:</div><div> </div><div> </div><blockquote style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left-color: rgb(204, 204, 204); border-left-width: 1px; border-left-style: solid; position: static; z-index: auto;" class="gmail_quote">
<div class="im">
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</div>this definition limits considerations to having two candidates only. In some special situations, like if circular rankings can be used, this definition seems to say that one votes A over B when one votes A>B>C>A (circular). </blockquote>
<div> </div><div>Sure, but that's ok, because, in your circular ranking, you're ranking A over B, even though you're circularly ranking each over the next.</div></div></div></div></blockquote><div><br></div><div>What I mean is that when all three candiates are considered, that circular ranking looks like a tie between those three. All three candidates are in a similar position, and the voter seems to find all three candidates equally good. The election method might not favour A over B based on this vote.</div><div><br></div><div>The definition also says that the voter votes A over B, B over C and C over A. Also relationship "voting X over Y" could thus be circular.</div><div><br></div><div>I wonder if this was your intention. This might work in your definition DC (?), but I'm not sure if thei is a good general definition of voting X over Y.</div><br><blockquote type="cite"><div dir="ltr"><div class="gmail_extra"><div class="gmail_quote"><div> </div><blockquote style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left-color: rgb(204, 204, 204); border-left-width: 1px; border-left-style: solid; position: static; z-index: auto;" class="gmail_quote">
The same could apply also in scenarios where the voter can give both (linear) rankings and approvals if they are independent of each other.<br></blockquote><div> </div><div>I don't know what an example of that would look like, bit it wouid probably likewise be ok.</div></div></div></div></blockquote><div><br></div><div>The situation is very similar. (I sent one example to you in a private mail. In that example the voter was able to rank the candidates A > B > C > D, and at the same time approve only D and B.)</div><div><br></div><div>Juho</div><div><br></div><br><blockquote type="cite"><div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">
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<div class="im"><br>
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> But in the event that there's a voting system that won't return a result with just one voter:<br>
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> Many voter definition of voting X over Y:<br>
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> A voter votes X over Y if s/he votes in such a way that, if X and Y were the only candidates, and if the voting system is the one in which s/he is voting, the addition of hir ballot, and 4 other identical ballots, to the ballot-set could change the winner from Y to X, but couldn't change the winner from X to Y.<br>
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> [end of many-voter definition of voting X over Y]<br>
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> That definition assumes that nonmonotonicity can't occur with only two candidates. If it could, then the immediately above-stated definition would have to be replaced by:<br>
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> A voter votes X over Y if s/he votes in such a way that, if X and Y were the only candidates, and if the voting system is the one in which s/he is voting, then the number of configurations of other voters in which the addtition of hir ballot, and 4 identical ones, would change the winner from Y to X, is greater than the number of configuration in which the addition of those ballots would change the winner from X to Y.<br>
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> [end of alternative many-voter definition of voting X over Y]<br>
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</div>I defined the idea behind effective ranking by referring to increasing the probability of becoming elected. Probabilities could be used also here (maybe easier and more exact).<br></blockquote><div> </div><div>Yes, for that many-voter definition, with the nonmonotonicity-protection (if that's needed), it's briefer to speak of increasing the probability that X will uniquely win, and it probably would work just as well. </div>
<div> </div><div>That substitution probably could, and maybe should, be made.</div><div> </div><div>Michael Ossipoff</div><div> </div><div> </div><div> </div><div> </div><div> </div><div> </div><div> </div><blockquote style="margin:0px 0px 0px 0.8ex;padding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;border-left-style:solid" class="gmail_quote">
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> Michael Ossipoff<br>
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