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<DIV style="RIGHT: auto" id=yiv85923900yui_3_2_0_16_131793875715643>I got the Woodall monotonicity criterion garbled. Instead of "mono-sub-delete" and then</DIV>
<DIV id=yiv85923900yui_3_2_0_16_1317938757156845>"mono-raise-delete", in both instances I meant *mono-sub-plump*. (I've made the corrections</DIV>
<DIV style="RIGHT: auto" id=yiv85923900yui_3_2_0_16_13179387571564997>in the text below.)<VAR id=yui-ie-cursor></VAR></DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571561085> </DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571561087>It means that candidate x shouldn't be harmed (i.e. have his probability of election reduced)</DIV>
<DIV style="RIGHT: auto" id=yiv85923900yui_3_2_0_16_13179387571561399>by swapping some ballots that don't have x top-ranked for some that rank x alone in top place</DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571561751>and ignore (or vote equal-bottom) all the other candidates.</DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571561937> </DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571561939>In the context of a universe of ballots that allow only strict ranking from the top, with truncation</DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562359>(but no other equal-ranking) allowed, Woodall defined it:</DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562842> </DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562844><snip></DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562737> </DIV><FONT size=2 face="Times New Roman"><FONT size=2 face="Times New Roman">
<DIV id=yiv85923900yui_3_2_0_16_13179387571562744>A candidate </FONT></FONT><I style="RIGHT: auto"><FONT size=2 face="Times New Roman"><FONT size=2 face="Times New Roman">x </I></FONT></FONT><FONT size=2 face="Times New Roman"><FONT size=2 face="Times New Roman">should not be harmed if:</DIV></FONT></FONT>
<DIV style="RIGHT: auto"> </DIV><FONT size=2 face=Arial><FONT size=2 face=Arial>
<DIV align=left>(</FONT></FONT><B><FONT size=2 face=Arial><FONT size=2 face=Arial>mono-sub-plump</B></FONT></FONT><FONT size=2 face=Arial><FONT size=2 face=Arial>) </FONT></FONT><FONT size=2 face="Times New Roman"><FONT size=2 face="Times New Roman">some ballots that do not have </FONT></FONT><I><FONT size=2 face="Times New Roman"><FONT size=2 face="Times New Roman">x </I></FONT></FONT><FONT size=2 face="Times New Roman"><FONT size=2 face="Times New Roman">top</DIV>
<DIV align=left>are replaced by ballots that have </FONT></FONT><I><FONT size=2 face="Times New Roman"><FONT size=2 face="Times New Roman">x </I></FONT></FONT><FONT size=2 face="Times New Roman"><FONT size=2 face="Times New Roman">top with no second</DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562754>choice;</DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562801> </DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562803><snip></DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562935> </DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562937> </DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571562782><A id=yiv85923900yui_3_2_0_16_13179387571564628 href="http://f1.grp.yahoofs.com/v1/4CSOTg18Jla8JeZD7lGf-L15LhewtDexi1BvIN9JQ79d6fDKQfZlI5ygNNqdMM_8b3XPbatc01XxYUjo1LgxMq9WirJdubA/wood1996.pdf" rel=nofollow target=_blank>http://f1.grp.yahoofs.com/v1/4CSOTg18Jla8JeZD7lGf-L15LhewtDexi1BvIN9JQ79d6fDKQfZlI5ygNNqdMM_8b3XPbatc01XxYUjo1LgxMq9WirJdubA/wood1996.pdf</A></DIV>
<DIV id=yiv85923900yui_3_2_0_16_13179387571564886> </DIV>
<DIV> </DIV></FONT></FONT>
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" id=yiv85923900yui_3_2_0_16_131793875715647 class=yiv85923900ms__id6338>
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" class=yiv85923900ms__id6340><FONT id=yiv85923900yui_3_2_0_16_131793875715674 size=2 face=Arial>Also I referred to "Push-over" strategy. That refers to the strategy of raising some weak candidate to enable </FONT></DIV>
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" id=yiv85923900yui_3_2_0_16_13179387571563673 class=yiv85923900ms__id6340><FONT id=yiv85923900yui_3_2_0_16_13179387571563678 size=2 face=Arial>some other candidate to win (or to have a better chance of winning).</FONT></DIV>
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" id=yiv85923900yui_3_2_0_16_13179387571563927 class=yiv85923900ms__id6340><FONT size=2 face=Arial></FONT> </DIV>
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" class=yiv85923900ms__id6340><FONT id=yiv85923900yui_3_2_0_16_13179387571563934 size=2 face=Arial>It was coined with methods like Top-Two Runoff and IRV in mind. Perhaps "Push-over *like* strategy" was <BR>more apt for the methods I referred to.<BR></FONT></DIV>
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<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" class="yiv85923900ms__id6340 ms__id488"><FONT size=2 face=Arial>Chris Benham</DIV></FONT>
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<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" class=yiv85923900ms__id6340><FONT id=yiv85923900yui_3_2_0_16_1317938757156412 size=2 face=Arial>---</FONT></DIV>
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<DIV><SPAN>I like this. Regarding how approval is inferred, I'm also happy with Forest's </SPAN><SPAN>idea of using Range </SPAN></DIV>
<DIV><SPAN>(aka Score) type ballots (on which voters give their most preferred candidates </SPAN><SPAN>the highest numerical <BR>scores) and interpreting any score above zero as approval and breaking approval </SPAN><SPAN>ties as any score</SPAN></DIV>
<DIV><SPAN>above 1 etc. Or any other sort of multi-slot ratings ballot where all except the bottom-most slot is</SPAN></DIV>
<DIV><SPAN>interpreted as approval.</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN>Another idea is to enter above-bottom equal-ranking between any 2 candidates in the pairwise matrix</SPAN></DIV>
<DIV><SPAN>as a whole vote for both candidates, and then take each candidate X's highest single pairwise score</SPAN></DIV>
<DIV><SPAN>as X's approval score.</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN id=yiv85923900yui_3_2_0_16_131793875715684>Here are a couple of examples to demonstrate how this method varies from some other Condorcet</SPAN></DIV>
<DIV><SPAN>methods.<BR><BR>48: A</SPAN></DIV>
<DIV><SPAN>01: A>D</SPAN></DIV>
<DIV><SPAN>24: B>D</SPAN></DIV>
<DIV><SPAN>27: C>B>D</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN>D is the most approved candidate and in the Smith set, and so Smith//Approval elects D.</SPAN></DIV>
<DIV><SPAN>Forest's "Enhanced DMC" or "Covering DMC" (and your suggested "SARR" implementation)</SPAN></DIV>
<DIV><SPAN>elects B.<BR></SPAN></DIV>
<DIV><SPAN>B covers D and to me looks like a better winner. This method has a weaker truncation incentive </SPAN></DIV>
<DIV id=yiv85923900yui_3_2_0_16_131793875715691><SPAN>than Smith//Approval.<BR></SPAN></DIV>
<DIV><SPAN>25: A>B</SPAN></DIV>
<DIV><SPAN id=yiv85923900yui_3_2_0_16_1317938757156378>27: B>C</SPAN></DIV>
<DIV><SPAN>26: C>A<BR>22: C<BR></SPAN></DIV>
<DIV><SPAN>Approvals: C75, B52, A51. A>B 51-49, B>C 52-48, C>A 75-25</SPAN><SPAN></DIV></SPAN>
<DIV id=yiv85923900yui_3_2_0_16_1317938757156100><SPAN></SPAN> </DIV>
<DIV><SPAN>Plain DMC and using MinMax or one of the algorithms that is equivalent to it when there are three</SPAN></DIV>
<DIV><SPAN>candidates (such as Schulze and Ranked Pairs and River) and weighing defeats either by Winning</SPAN></DIV>
<DIV><SPAN>Votes or Margins all elect B.</SPAN></DIV>
<DIV id=yiv85923900yui_3_2_0_16_1317938757156105><SPAN></SPAN> </DIV>
<DIV id=yiv85923900yui_3_2_0_16_1317938757156271><SPAN id=yiv85923900yui_3_2_0_16_1317938757156276>If 5 of the 22 C voters change to A those methods all elect C (a failure of Woodall's "mono-sub-plump"</SPAN></DIV>
<DIV><SPAN>criterion).</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV><SPAN></SPAN><SPAN>
<DIV><SPAN>25: A>B</SPAN></DIV>
<DIV><SPAN>27: B>C</SPAN></DIV>
<DIV><SPAN>26: C>A<BR>17: C<BR></SPAN></DIV>
<DIV><SPAN>05: A (was C)</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN>Approvals: C70, A56, B52. A>B 56-49, B>C 52-48, C>A 70-30.</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV id=yiv85923900yui_3_2_0_16_1317938757156324><SPAN>In both cases our favoured method (like Smith//Approval) elects C, the positionally dominant candidate. It <BR>seems those other </SPAN><SPAN>methods are more vulnerable to Push-over strategy.</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV id=yiv85923900yui_3_2_0_16_1317938757156101><SPAN id=yiv85923900yui_3_2_0_16_131793875715677>(To be fair, Woodall has demonstrated that no Condorcet method can meet mono-sub-plump)</SPAN></SPAN><SPAN id=yiv85923900yui_3_2_0_16_1317938757156158> </SPAN></DIV>
<DIV><SPAN id=yiv85923900yui_3_2_0_16_1317938757156334></SPAN> </DIV>
<DIV><SPAN id=yiv85923900yui_3_2_0_16_1317938757156337>Chris Benham</DIV></SPAN>
<DIV><BR></DIV>
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<DIV style="BORDER-BOTTOM: #ccc 1px solid; BORDER-LEFT: #ccc 1px solid; PADDING-BOTTOM: 0px; LINE-HEIGHT: 0; MARGIN: 5px 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; HEIGHT: 0px; FONT-SIZE: 0px; BORDER-TOP: #ccc 1px solid; BORDER-RIGHT: #ccc 1px solid; PADDING-TOP: 0px" class=yiv85923900hr></DIV><B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Ted Stern <araucaria.araucana@gmail.com><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> election-methods@lists.electorama.com<BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> Forest Simmons <fsimmons@pcc.edu>; Chris Benham <cbenhamau@yahoo.com.au><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Wednesday, 5 October 2011 8:35 AM<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [EM] Enhanced DMC<BR></FONT><BR>After some private email exchanges with Forest and Chris, I'm<BR>proposing a simple way of implementing Enhanced DMC, plus a new name,<BR>Strong Approval Round
Robin Voting (SARR Voting).<BR><BR>Ballot:<BR><BR>Ranked Voting, all explicitly ranked candidates considered approved.<BR>Equal ranking allowed. I'm basing this on recommendation from Chris<BR>Benham. I'm open to alternatives, but it seems to be the easiest way<BR>to do it for now, and the most resistant to burying strategies.<BR><BR>Tallying:<BR><BR>Form the pairwise matrix, using the standard Condorcet procedure. In<BR>the diagonal entries, save total Approval votes.<BR><BR>For N candidates, the list of candidates in order from highest to<BR>lowest approval is<BR><BR> X_0, X_1, ..., X_k, X_{k+1}, ..., X_{N-1}<BR><BR>Initialize the Strong set to the empty set<BR><BR>Initialize the Weak set to the empty set.<BR><BR>For k = 0 to N-1,<BR><BR> If X_k is already in the Weak set, continue iterating. (X_k is<BR> defeated by a higher approved candidate. This is called being<BR> "strongly
defeated".)<BR><BR> If X_k loses to a member of the Weak set, continue iterating. (X_k<BR> may defeat all higher approved candidates, but is "weakly defeated"<BR> by at least one of them.)<BR> <BR> If we're still here in the loop, X_k defeats all candidates in the<BR> Strong Set and all candidates in the Weak set. (X_k "covers" all<BR> previously added members of the Strong set.)<BR><BR> Add X_k to the Strong set and add all of X_k's defeats to the Weak<BR> set.<BR><BR> Set the provisional winner to X_k.<BR><BR>The last provisional winner (the last candidate added to the Strong<BR>set) is the winner of the election.<BR><BR>Note:<BR><BR>The first member of the Strong Set will be X_0.<BR><BR>It is easiest to do this by hand if you first permute the pairwise<BR>array so that it follows the same X_0, ..., X_{N-1} ordering.<BR><BR>As an example election, consider the one on this
page:<BR><BR> <A href="http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting" rel=nofollow target=_blank>http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting</A><BR><BR>Iterating through E, A, C, B, D, we find<BR><BR> E: Strong and Weak Sets are empty, so E has no losses to either.<BR><BR> Strong set = {E}; Weak set = {C, D}<BR> <BR> Provisional winner set to E.<BR><BR> A: A defeats Strong set {E} and Weak set {C, D}.<BR><BR> => Strong set = {E, A}; Weak set = {C, D}<BR><BR> Provisional winner set to A.<BR><BR> C: in Weak set, not added to Strong set.<BR><BR> B: Defeats A, but is defeated by D from Weak set (and is therefore<BR> "weakly defeated" by A).<BR><BR> D: in Weak set, not added to Strong set.<BR><BR>A is
the last candidate added to the Strong set, so A wins.<BR><BR>Ted<BR>-- <BR>araucaria dot araucana at gmail dot com<BR><BR>On 26 Sep 2011 11:44:13 -0700, Chris Benham wrote:<BR>><BR>> Forest,<BR>><BR>> "I think in general that if the approval scores are at all valid I<BR>> would go for the enhanced DMC winner over any of the chain building<BR>> methods we have considered. I think other considerations over-ride<BR>> the importance of being uncovered." <BR><BR>> I agree.<BR>><BR>> I think the chain<BR>> building method in comparison seems a bit arbitrary and less<BR>> philosophically justified.<BR>> <BR>> Also the method has a fairly<BR>> straight-forward description that doesn't need to mention "Smith<BR>> set" or "the Condorcet winner". So of these similar methods<BR>> (that include Smith//Approval and all elect the same winner if the<BR>> Smith set contains 3 members or 1 member),
I think this is my<BR>> favourite. Maybe it could use a new name :)<BR>><BR>> Chris<BR>> <BR>> <BR>> <BR>><BR>> From: "<A href="mailto:fsimmons@pcc.edu" rel=nofollow target=_blank ymailto="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</A>" <<A href="mailto:fsimmons@pcc.edu" rel=nofollow target=_blank ymailto="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</A>><BR>> To: C.Benham <<A href="mailto:cbenhamau@yahoo.com.au" rel=nofollow target=_blank ymailto="mailto:cbenhamau@yahoo.com.au">cbenhamau@yahoo.com.au</A>><BR>> Cc: <A href="mailto:election-methods-electorama.com@electorama.com" rel=nofollow target=_blank ymailto="mailto:election-methods-electorama.com@electorama.com">election-methods-electorama.com@electorama.com</A><BR>> Sent: Monday, 12 September 2011 8:50 AM<BR>> Subject: Re: Enhanced DMC<BR>><BR>> Very good Chris. <BR>><BR>> I tried to build a
believable profile of ballots that would yield the approval order and defeats of this <BR>> example without success, but I am sure that it is not impossible.<BR>><BR>> I think in general that if the approval scores are at all valid I would go for the enhanced DMC winner over <BR>> any of the chain building methods we have considered. I think other considerations over-ride the <BR>> importance of being uncovered.<BR>><BR>> ----- Original Message -----<BR>> From: "C.Benham" <BR>> Date: Sunday, September 11, 2011 10:08 am<BR>> Subject: Enhanced DMC<BR>> To: <A href="mailto:election-methods-electorama.com@electorama.com" rel=nofollow target=_blank ymailto="mailto:election-methods-electorama.com@electorama.com">election-methods-electorama.com@electorama.com</A><BR>> Cc: Forest W Simmons <BR>><BR>>> Forest Simmons wrote (15 Aug 2011):<BR>>> <BR>>> >Here's a possible scenario:<BR>>>
><BR>>> >Suppose that approval order is alphabetical from most approval <BR>>> to least A, B, C, D.<BR>>> ><BR>>> >Suppose further that pairwise defeats are as follows:<BR>>> ><BR>>> >C>A>D>B>A together with B>C>D .<BR>>> ><BR>>> >Then the set P = {A, B} is the set of candidates neither of <BR>>> which is pairwise<BR>>> >beaten by anybody with greater approval.<BR>>> ><BR>>> >Since the approval winner A is not covered by B, it is not <BR>>> covered by any<BR>>> >member of P, so the enhanced version of DMC elects A.<BR>>> ><BR>>> >But A is covered by C so it cannot be elected by any of the <BR>>> chain building<BR>>> >methods that elect only from the uncovered set.<BR>>> ><BR>>> <BR>>> Forest,<BR>>> <BR>>> Is the "Approval Chain-Building" method the same
as simply <BR>>> electing the <BR>>> most approved uncovered candidate <BR>>> <BR>>> I surmise that the set of candidates not pairwise beaten by a <BR>>> more <BR>>> approved candidate (your set "P", what I've<BR>>> been referring to as the "Definite Majority set") and the <BR>>> Uncovered set <BR>>> don't necessarily overlap.<BR>>> <BR>>> If forced to choose between electing from the Uncovered set and <BR>>> electing <BR>>> from the "DM" set, I tend towards<BR>>> the latter.<BR>>> <BR>>> Since Smith//Approval always elects from the DM set, and your <BR>>> suggested <BR>>> "enhanced DMC" (elect the most<BR>>> approved member of the DM set that isn't covered by another <BR>>> member) <BR>>> doesn't necessarily elect from the Uncovered set;<BR>>> there doesn't seem to be any obvious philosophical case that <BR>>>
enhanced <BR>>> DMC is better than Smith//Approval.<BR>>> <BR>>> (Also I would say that an election where those two methods <BR>>> produce <BR>>> different winners would be fantastically unlikely.)<BR>>> <BR>>> A lot of Condorcet methods are promoted as being able to give <BR>>> the <BR>>> winner just from the information contained in the<BR>>> gross pairwise matrix. I think that the same is true of these <BR>>> methods <BR>>> if we take a candidate X's highest gross pairwise<BR>>> score as X's approval score. Can you see any problem with that <BR>>> <BR>>> <BR>>> Chris Benham<BR>>> <BR>>> <BR>>> <BR>>> <BR>>> ----- Original Message -----<BR>>> From:<BR>>> Date: Friday, August 12, 2011 3:12 pm<BR>>> Subject: Enhanced DMC<BR>>> To: election-methods at lists.electorama.com,<BR>>> <BR>>> > >
From: "C.Benham"<BR>>> > > To: election-methods-electorama.com at electorama.com<BR>>> > > Subject: [EM] Enhanced DMC<BR>>> ><BR>>> > > Forest,<BR>>> > > The "D" in DMC used to stand for *Definite*.<BR>>> ><BR>>> > Yeah, that's what we finally settled on.<BR>>> ><BR>>> > ><BR>>> > > I like (and I think I'm happy to endorse) this Condorcet method<BR>>> > > idea, and consider it to be clearly better than regular DMC<BR>>> > ><BR>>> > > Could this method give a different winner from the ("Approval<BR>>> > > Chain Building" ) method you mentioned in the "C//A" thread <BR>>> (on 11<BR>>> > > June 2011) <BR>>> ><BR>>> > Yes, I'll give an example when I get more time. But for all <BR>>> practical <BR>>> > purposes they both pick the highest approval
Smith candidate.<BR>>> <BR>>> <BR>>> <BR>>> Here's a possible scenario:<BR>>> <BR>>> Suppose that approval order is alphabetical from most approval <BR>>> to least <BR>>> A, B, C, D.<BR>>> <BR>>> Suppose further that pairwise defeats are as follows:<BR>>> <BR>>> C>A>D>B>A together with B>C>D .<BR>>> <BR>>> Then the set P = {A, B} is the set of candidates neither of <BR>>> which is <BR>>> pairwise<BR>>> beaten by anybody with greater approval.<BR>>> <BR>>> Since the approval winner A is not covered by B, it is not <BR>>> covered by any<BR>>> member of P, so the enhanced version of DMC elects A.<BR>>> <BR>>> But A is covered by C so it cannot be elected by any of the <BR>>> chain building<BR>>> methods that elect only from the uncovered set.<BR>>> <BR>>> <BR>>> Forest
Simmons wrote (12 June 2011):<BR>>> <BR>>> > I think the following complete description is simpler than anything<BR>>> > possible for ranked pairs:<BR>>> ><BR>>> > 1. Next to each candidate name are the bubbles (4) (2) (1). The<BR>>> > voter rates a candidate on a scale from<BR>>> > zero to seven by darkening the bubbles of the digits that add <BR>>> up to<BR>>> > the desired rating.<BR>>> ><BR>>> > 2. We say that candidate Y beats candidate Z pairwise iff Y <BR>>> is rated<BR>>> > above Z on more ballots than not.<BR>>> ><BR>>> > 3. We say that candidate Y covers candidate X iff Y pairwise beats<BR>>> > every candidate that X pairwise<BR>>> > beats or ties.<BR>>> ><BR>>> > [Note that this definition implies that if Y covers X, then Y <BR>>> beats X<BR>>> > pairwise, since X ties
X pairwise.]<BR>>> ><BR>>> > Motivational comment: If a method winner X is covered, then the<BR>>> > supporters of the candidate Y that<BR>>> > covers X have a strong argument that Y should have won instead.<BR>>> ><BR>>> > Now that we have the basic concepts that we need, and <BR>>> assuming that<BR>>> > the ballots have been marked<BR>>> > and collected, here's the method of picking the winner:<BR>>> ><BR>>> > 4. Initialize the variable X with (the name of) the <BR>>> candidate that<BR>>> > has a positive rating on the greatest<BR>>> > number of ballots. Consider X to be the current champion.<BR>>> ><BR>>> > 5. While X is covered, of all the candidates that cover X, <BR>>> choose the<BR>>> > one that has the greatest number of<BR>>> > positive ratings to become the new champion X.<BR>>>
><BR>>> > 6. Elect the final champion X.<BR>>> ><BR>>> > 7. If in step 4 or 5 two candidates are tied for the number of<BR>>> > positive ratings, give preference (among the<BR>>> > tied) to the one that has the greatest number of ratings <BR>>> above level<BR>>> > one. If still tied, give preference<BR>>> > (among the tied) to the one with the greatest number of <BR>>> ratings above<BR>>> > the level two. Etc.<BR>>> ><BR>>> > Can anybody do a simpler description of any other Clone Independent<BR>>> > Condorcet method?<BR>>> <BR>>> <BR>>> <BR>>> <BR>> -------------- next part --------------<BR>> An HTML attachment was scrubbed...<BR>> URL: <<A href="http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20110926/a10be831/attachment.htm" rel=nofollow
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