<div>Hi Juho,</div>
<div> </div>
<div>I am sending two corrections to my email below and a fourth formulation of the approval cutoff. </div>
<div>I mixed up Rule 2 and Rule 1. My appologies for the spamming.</div>
<div> </div>
<div>In order to avoid further mistakes, </div>
<div>I call Rule 1 the "Absolute approval cutoff" or "A beats max(X,B) for all B". Rule 1 has three different formulations 1a, 1b and 1c.</div>
<div>I call Rule 2 the "Approval cutoff" or "A beats X". Rule 2 has also three different formulations 2a, 2b and 2c. Better names for the cut-off rules are greeted.</div>
<div> </div>
<div>I wrote below:</div>
<div>"...each member of the smith set will have have to obey rule 2 and if none of them does, obey rule 1 and if none of them does proceed as normal."</div>
<div> </div>
<div>Correction 1: Rule 1 should be Rule 2 and vice versa in the text above.</div>
<div>Thus the text above should read:</div>
<div>"...each member of the Smith set will have have to satisfy Rule 1 (the absolute approval cutoff) and if none of them does, satisfy Rule 2 (the approval cutoff)."</div>
<div> </div>
<div>---</div>
<div>I wrote below:</div>
<div>> Thus the Woodall method, which goes: "Score candidates according to the Hare</div>
<div>> [IRV] elimination order, and chose the Smith set candidate with best score",</div>
<div>> could be modified to read:</div>
<div>> "Score candidates according to the Hare [IRV] elimination order, and chose</div>
<div>> the Smith set candidate which satisfies rule 2 with the best score. If</div>
<div>> no such candidate exists chose the Smith set candidate which satisfies rule</div>
<div>> 1 with the best score."</div>
<div> </div>
<div>Correction 2: Rule 1 should be Rule 2 and vice versa in the text above.</div>
<div>Woodalls' hybrid method should thus be modified as follows:</div>
<div>"Score candidates according to the Hare [IRV] elimination order, and chose the Smith set candidate which satisfies Rule 1 (the absolute approval cutoff) with the best score. If no such candidate exists, chose the Smith set candidate which satisfies Rule 2 (the approval cutoff) with best score."</div>
<div> </div>
<div>I don't know if the absolute majority criterion really is needed.</div>
<div> </div>
<div> </div>
<div>Best regards</div>
<div>Peter Zborník</div>
<div> </div>
<div>On Thu, Jun 2, 2011 at 6:10 PM, Peter Zbornik <<a href="mailto:pzbornik@gmail.com">pzbornik@gmail.com</a>> wrote:</div>
<div>> Hi Juho,</div>
<div>> </div>
<div>> I am sending a two corrections:</div>
<div>> </div>
<div>> ----</div>
<div>> </div>
<div>> I wrote below:</div>
<div>> "Rule 2 (from the generalized ballot):</div>
<div>> A winning candidate needs to be explicitly ranked on >50% of the ballots.</div>
<div>> This rule amounts to "A majority of all voters support the election of A</div>
<div>> rather than having no election winner". Technically this rule means that any</div>
<div>> candidate A has to win the election of A vs X in order to have a chance of</div>
<div>> winning the election."</div>
<div>> </div>
<div>> That was not entirely unambigous, as Kristoffer pointed out.</div>
<div>> </div>
<div>> Rule 2 can be formulated as three different rules:</div>
<div>> </div>
<div>> Rule 2a. The election winner A needs to be ranked above X on >50% of the</div>
<div>> votes (A>X or approved by >50% of the votes).</div>
<div>> </div>
<div>> Rule 2b: The election winner needs to beat X head-to-head (A>=X, weak</div>
<div>> approval, allowing for neutral stances, "=" with 0.5 votes for X and A).</div>
<div>> </div>
<div>> Rule 2c: The election winner wins a Condorcet election, which includes X.</div>
<div>> </div>
<div>> ---</div>
<div>> </div>
<div>> In rules 2a and 2b, X is ranked on the ballot (either explicitly or</div>
<div>> implicitly) but is not a candidate in the election.</div>
<div>> In rule 2c, X is a candidate in the election.</div>
<div>> </div>
<div>> Rules 2b and 2c are equivalent in IRV (in the round A vs X, which occurs</div>
<div>> after the IRV winner gets the votes of the runner-up B where B>A ).</div>
<div>> Rules 2a, 2b and 2c are equivalent in IRV, if the voter is not allowed</div>
<div>> to rank X equal to A (X=A or A neutral).</div>
<div>> </div>
<div>> To see that Rule 2a is not equivalent to Rule 2b.</div>
<div>> Compare the election:</div>
<div>> 2:A=X</div>
<div>> 2:A>X</div>
<div>> 1:X>A</div>
<div>> According to Rule 2a A does not win the election (X doesn't win either</div>
<div>> though)</div>
<div>> According to Rule 2b A beats X and thus wins.</div>
<div>> </div>
<div>> Rule 2c is probably different from rule 2b as Kristoffer pointed, but we</div>
<div>> don't have an example to prove it yet. Such an example probably requires</div>
<div>> four candidates, including X, where the winner doesn't beat X in the</div>
<div>> pairwise comparison.</div>
<div>> </div>
<div>> Rule 2c does not require extra rules "outside" the Condorcet election a has</div>
<div>> some nice properties coming out from it - margins and winning votes are</div>
<div>> equal and have the same pairwise comparison matrix if we use soccer scoring</div>
<div>> (0.5 wins each for a tie using winning votes).</div>
<div>> </div>
<div>> With rule 2c, the election has always a winner, even though the winner can</div>
<div>> be the vacant seat, which also is a nice "completeness" property (or</div>
<div>> whatever that is called). With the other approval rules we can have a tie</div>
<div>> where none of the candidates wins.</div>
<div>> </div>
<div>> Rule 2c is not possible to substitute with explicit cut-offs, as A can win</div>
<div>> the Condorcet election even though X beats A, i.e. A has less than 50% of</div>
<div>> the preferences and conversly X can win the election even though A beats X,</div>
<div>> i.e. the election will not have a winner even though A is preferred before</div>
<div>> no winner on >50% of the votes.</div>
<div>> </div>
<div>> Rule 2a and 2b are simpler to understand than 2c, but require an extra rule</div>
<div>> "outside" the Condorcet election.</div>
<div>> </div>
<div>> I have no special preference between the formulation of the rules 1a, 1,b or</div>
<div>> 1c and 2a, 2b or 2c. Each one of them have their pros and cons depending on</div>
<div>> what they will be used for.</div>
<div>> </div>
<div>> ---</div>
<div>> </div>
<div>> I wrote below:</div>
<div>> "Rule 1 [...]</div>
<div>> In a pairwise comparison of a Condorcet election (or in the final round of</div>
<div>> an IRV election), a winning candidate needs to get >50% of the total votes</div>
<div>> (including blank votes). This rule amounts to: "A majority of all voters</div>
<div>> support A before B". Technically this is a three part election with A vs B+X</div>
<div>> and B vs A+X. Thus we can have elections with no winner."</div>
<div>> </div>
<div>> That was also not entirely unambiguous.</div>
<div>> </div>
<div>> Rule 1 can be formulated as three different rules, anogously to rule 2:</div>
<div>> </div>
<div>> Rule 1a. The election winner A needs also to be strictly preferred to both B</div>
<div>> and X on >50% of the votes in the pairwise conparison (A>B and A>X have</div>
<div>> both to be true for A to get a vote in A vs B). A vote for A in A vs B is</div>
<div>> not A=B>X nor X>A>B or the blank vote.</div>
<div>> This rule is the same as strictly approving A before B and X.</div>
<div>> </div>
<div>> Rule 1b. The election winner A needs to be weakly preferred to both B and</div>
<div>> X on >50% of the votes in the pairwise comparison (A gets one vote in A vs B</div>
<div>> if A>B and A>X, and half a vote in other cases where A>=B and A>=X).</div>
<div>> This rule is the same as weakly approving A before B and X (i.e allowing to</div>
<div>> be neutral, "=", which counts as half a win).</div>
<div>> </div>
<div>> Rule 1c. Instead of writing "A>B and A>X", one might write "A>max(B,X)",</div>
<div>> where max(B,X)=B, if B>=X and max(B,X)=X. if X>B. Rule 1c states, that the</div>
<div>> election winner A needs to beat the compounded candidates Y1=max(B1,X),...,</div>
<div>> Yk=max(Bk,X), in a Condorcet election, with the candidates A, B1,...Bk.</div>
<div>> </div>
<div>> Applying Rule 1c, we might talk about an absolute majority Smith set where</div>
<div>> its members win according to rule 1 against the other candidates.</div>
<div>> ---</div>
<div>> </div>
<div>> In rules 1a and 1b, X is ranked on the ballot (either explicitly or</div>
<div>> implicitly) but is not a candidate in the election.</div>
<div>> In rule 1c, max(X,B) is a candidate in the election.</div>
<div>> </div>
<div>> Rules 1 and 2 satisfy Woodall's plurality criterion</div>
<div>> </div>
<div>> Rules 1b and 1c are equivalent in IRV (last round).</div>
<div>> Rules 1a, 1b and 1c are equivalent in IRV, if the voter is not allowed</div>
<div>> to rank X and B equal to A (A=X and A=B are not allowed), i.e. if equalities</div>
<div>> are not allowed.</div>
<div>> </div>
<div>> To see that Rule 1a is not equivalent to Rule 1b.</div>
<div>> Consider the election:</div>
<div>> 2:A=B>X</div>
<div>> 3:A>B>X</div>
<div>> 1:B>A>X</div>
<div>> 1:X>A=B</div>
<div>> </div>
<div>> We have the election A vs Y (Y=max(B,X))</div>
<div>> 2:A=Y</div>
<div>> 3:A>Y</div>
<div>> 1:Y>A</div>
<div>> 1:Y>A</div>
<div>> According to Rule 1a: A is strictly preferred to B and X on 3 ballots out of</div>
<div>> 7. A doesn't win.</div>
<div>> According to Rule 1b A wins with 4 votes to 7.</div>
<div>> </div>
<div>> Rule 1c is probably different from rule 1b as Kristoffer pointed, but we</div>
<div>> don't have an example to prove it yet. Such an example probably requires</div>
<div>> five candidates, including X, where the winner A doesn't beat max(Bi,X) the</div>
<div>> pairwise comparison for some i, 1<i<k, in .</div>
<div>> </div>
<div>> ---</div>
<div>> </div>
<div>> After reading the paper on hybrid methods, that Kristofer</div>
<div>> recomended (<a href="http://www.votingmatters.org.uk/FORTHCOMING/I29P1f.pdf">http://www.votingmatters.org.uk/FORTHCOMING/I29P1f.pdf</a>), the</div>
<div>> hybrid IRV-Condorcet methods (Woodall, Benham, Smith-Hare and Tideman) could</div>
<div>> be adjusted to accomodate the empty vote, similarly as I propose for IRV, so</div>
<div>> that each member of the smith set will have have to obey rule 2 and if none</div>
<div>> of them does, obey rule 1 and if none of them does proceed as normal.</div>
<div>> </div>
<div>> Thus the Woodall method, which goes: "Score candidates according to the Hare</div>
<div>> [IRV] elimination order, and chose the Smith set candidate with best score",</div>
<div>> could be modified to read:</div>
<div>> "Score candidates according to the Hare [IRV] elimination order, and chose</div>
<div>> the Smith set candidate which satisfies rule 2 with the best score. If</div>
<div>> no such candidate exists chose the Smith set candidate which satisfies rule</div>
<div>> 1 with the best score."</div>
<div>> </div>
<div>> ---</div>
<div>> </div>
<div>> Juho, I like your approach to translate the ballot to normal language.</div>
<div>> That's the way to go.</div>
<div>> We need to translate the "ballot code" to language that everybody</div>
<div>> understands.</div>
<div>> No abstract playing with numbers and apocryphic ballot code words, if they</div>
<div>> are not absolutely needed.</div>
<div>> Maybe there could be several shorthand options spelt out for the most common</div>
<div>> ballot choices and on the same time the full expressiveness of the</div>
<div>> generalized ballot could be retained for voter who request it. </div>
<div>> </div>
<div>> Best regards</div>
<div>> Peter Zborník</div>
<div>> </div>
<div>> On Tue, May 31, 2011 at 6:52 PM, Peter Zbornik <<a href="mailto:pzbornik@gmail.com">pzbornik@gmail.com</a>> wrote:</div>
<div>>></div>
<div>>> Juho,</div>
<div>>> </div>
<div>>> a correction:</div>
<div>>> I wrote: "If a candidate is ranked on >50% of the ballots, then this</div>
<div>>> method will always produce a winner"</div>
<div>>> </div>
<div>>> That is not correct. Say we have 4 A>B, 3 B>A, 3 blank.</div>
<div>>> Noone wins that election in the modified IRV election I proposed, neither</div>
<div>>> candidate has 50% of the total vote in the first and final round, but both</div>
<div>>> candidates are explicitly ranked on >50% of the ballots.</div>
<div>>> </div>
<div>>> The example above illustrates the difference between the two rules I</div>
<div>>> proposed for blank voting in Condorcet elections in my previous emails. I</div>
<div>>> restate the rules again:</div>
<div>>> </div>
<div>>> Rule 1 (proposed above):</div>
<div>>> In a pairwise comparison of a Condorcet election (or in the final round of</div>
<div>>> an IRV election), a winning candidate needs to get >50% of the total votes</div>
<div>>> (including blank votes). This rule amounts to: "A majority of all voters</div>
<div>>> support A before B". Technically this is a three part election with A vs B+X</div>
<div>>> and B vs A+X. Thus we can have elections with no winner.</div>
<div>>> </div>
<div>>> Rule 2 (from the generalized ballot):</div>
<div>>> A winning candidate needs to be explicitly ranked on >50% of the ballots.</div>
<div>>> This rule amounts to "A majority of all voters support the election of A</div>
<div>>> rather than having no election winner". Technically this rule means that any</div>
<div>>> candidate A has to win the election of A vs X in order to have a chance of</div>
<div>>> winning the election.</div>
<div>>> </div>
<div>>> If the proposed method (call it Static-IRV) fails to produce a winner</div>
<div>>> (i.e. all IRV winners, who don't satisfy Rule 1 above are deleted), then the</div>
<div>>> IRV election would be repeated only for candidates having least 50% of</div>
<div>>> explicit ballot rankings (applying rule 2 instead of rule 1). If no</div>
<div>>> candidate has at least 50% of explicit ballot rankings, then the IRV winner</div>
<div>>> would be elected.</div>
<div>>> </div>
<div>>> The same heuristic could be applied for Condorcet elections.</div>
<div>>> </div>
<div>>> Heuristics are frowned upon, I know, but even Schulze uses heuristics, and</div>
<div>>> a lot of them.</div>
<div>>> </div>
<div>>> The benefits of the proposed Static-IRV election method is</div>
<div>>> 1] to keep the LNH property as long as possible and</div>
<div>>> 2] respect the blank vote and get a winner with 50% of all votes in the</div>
<div>>> last round (the run-off), if possible</div>
<div>>> 3] to generate candidates with strong support for the runoff</div>
<div>>> </div>
<div>>> IRV can be seen as a heuristic to generate two good candidates for a</div>
<div>>> head-to-head election.</div>
<div>>> </div>
<div>>> If the blank vote is not respected and the winner is not required to have</div>
<div>>> 50% of the vote, then we have a plurality voting system.</div>
<div>>> </div>
<div>>> In the Czech senatorial elections, it is not possible to vote blank in the</div>
<div>>> second round and some senators are elected with less than 50% support of the</div>
<div>>> voters, counting "invalid" votes and abstentions.</div>
<div>>> If blank votes were allowed in the second round of run-off elections, then</div>
<div>>> double-voting could be allowed too (A=B, half a vote to each) and possible</div>
<div>>> allowing for ranking of the candidates (A>B) in order to allow the voters to</div>
<div>>> compensate the blank votes.</div>
<div>>> </div>
<div>>> In the Czech parliament, >50% of the votes (including abstentions) is</div>
<div>>> required for a decision.</div>
<div>>> A good argument for the blank vote and for the 50% requirement in</div>
<div>>> elections is to refer to the voting in parliament.</div>
<div>>> </div>
<div>>> Do you know of any nice paper or post on this list, which discusses</div>
<div>>> possible significant modifications/improvement of the general mechanics</div>
<div>>> of Condorcet elections (apart from the debate on ranked-pairs, maximin,</div>
<div>>> minimax, Schulze, Beatpath, Copeland etc.)?</div>
<div>>> </div>
<div>>> Best regards</div>
<div>>> Peter Zborník</div>
<div>>> </div>
<div>>> </div>
<div>>> On Tue, May 31, 2011 at 11:58 AM, Peter Zbornik <<a href="mailto:pzbornik@gmail.com">pzbornik@gmail.com</a>></div>
<div>>> wrote:</div>
<div>>>></div>
<div>>>> Juho,</div>
<div>>>> </div>
<div>>>> comments in the text below.</div>
<div>>>> Mostly details.</div>
<div>>>> </div>
<div>>>> Below I propose a new election method using IRV, which is closer to</div>
<div>>>> Condorcet than regular IRV and would have elected Montroll in Burlington.</div>
<div>>>> </div>
<div>>>> Method:</div>
<div>>>> If the IRV winner doesn't get >50% of the votes (including blank ballots</div>
<div>>>> or "write-in candidates") then he/she is deleted and the IRV election is</div>
<div>>>> re-run on the same ballots without the candidate.</div>
<div>>>> Repeat until we have a winner with >50%.</div>
<div>>>> If no candidate is ranked on >50% of the ballots, then a new election is</div>
<div>>>> called.</div>
<div>>>> If a candidate is ranked on >50% of the ballots, then this method will</div>
<div>>>> always produce a winner</div>
<div>>>> </div>
<div>>>> That would be, I think the smallest improvement on IRV, which could make</div>
<div>>>> a positive change in real life and would support centrist candidates.</div>
<div>>>> </div>
<div>>>> The generalized ballot completion procedure will not work in an IRV-STV</div>
<div>>>> election, I think, but adding null-candidates at the end of the empty</div>
<div>>>> ballot will work, if the null-candidate cannot be deleted. However static</div>
<div>>>> quotas is easier to understand in IRV-STV, than null candidates, I think. I</div>
<div>>>> cannot see how to integrate negative rankings in STV elections.</div>
<div>>>> </div>
<div>>>> The rest in the text below</div>
<div>>>> </div>
<div>>>> Best regards</div>
<div>>>> Peter Zborník</div>
<div>>>></div>
<div>>>> On Tue, May 31, 2011 at 12:19 AM, Juho Laatu <<a href="mailto:juho4880@yahoo.co.uk">juho4880@yahoo.co.uk</a>></div>
<div>>>> wrote:</div>
<div>>>>></div>
<div>>>>> On 30.5.2011, at 18.41, Peter Zbornik wrote:</div>
<div>>>>></div>
<div>>>>> Juho,</div>
<div>>>>> </div>
<div>>>>> summarize my argument concerning generalized ballot and generalized</div>
<div>>>>> ballot completion and in the end of this email I suggest a new single-member</div>
<div>>>>> Condorcet election system.</div>
<div>>>>> </div>
<div>>>>> Nomenclature: I think that "null-candidate" (marked "X") is a fitting</div>
<div>>>>> name for voting for not filling a seat. The other names given do not have</div>
<div>>>>> that chique mathematical sound: "White", "None of the Above", "Re-open</div>
<div>>>>> nominations", "Ficus (the plant)", etc.</div>
<div>>>>> </div>
<div>>>>> In the discussion, I think I showed the following</div>
<div>>>>> If blank voting ("null candidates") is not allowed, then</div>
<div>>>>> truncated/incomplete ballots give different election results for winning</div>
<div>>>>> votes and for margins.</div>
<div>>>>> Compare Kevin Venzke's example:</div>
<div>>>>> 35:A>B</div>
<div>>>>> 25:B</div>
<div>>>>> 40:C</div>
<div>>>>> If we complete this election (Woodall's original proposal) to</div>
<div>>>>> 35:A>B>C</div>
<div>>>>> 25:B>A=C</div>
<div>>>>> 40:C>A=B,</div>
<div>>>>> then the election gives different results whether the candidates in the</div>
<div>>>>> ties are resolved as 0.5 vs 0.5 (margins - A winner) or 0 vs 0 (winning</div>
<div>>>>> votes - B winner)</div>
<div>>>>> (compare the results of the election at</div>
<div>>>>> <a href="http://condorcet.ericgorr.net/">http://condorcet.ericgorr.net/</a> and</div>
<div>>>>> <a href="http://www1.cse.wustl.edu/~legrand/rbvote/calc.html">http://www1.cse.wustl.edu/~legrand/rbvote/calc.html</a>)</div>
<div>>>>> </div>
<div>>>>> For margins, Woodall's plurality criterion is violated.</div>
<div>>>>> </div>
<div>>>>> If the same election is completed to allow for blank voting:</div>
<div>>>>> 35:A>B>X>C</div>
<div>>>>> 25:B>X>A=C</div>
<div>>>>> 40:C>X>A=B,</div>
<div>>>>> then the election gives same result (B - winner) both for margins and</div>
<div>>>>> for winning votes and the parwise comparison matrix will be identical for</div>
<div>>>>> both methods if a an equality awarded 0.5 votes for both candidates.</div>
<div>>>>></div>
<div>>>>> To summarize my thoughts...</div>
<div>>>>> - I think explicit cutoffs work fine when the cutoff carries some agreed</div>
<div>>>>> message (e.g. approved vs. not approved)</div>
<div>>>>> - Using explicit cutoff just as an extra candidate that voters can use</div>
<div>>>>> as a strategic tool to generate big defeats to some candidates is more</div>
<div>>>>> problematic (you can try to bury someone under X without any risk of</div>
<div>>>>> electing X)</div>
<div>>>></div>
<div>>>> You can try to bury someone under all other candidates anyway.</div>
<div>>>> Introducing a null-candidate as a "cuttoff" does not change that.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> - Implicit cutoff is problematic since it may encourage truncation</div>
<div>>>>> - Woodall's plurality criterion assumes an implicit cutoff (i.e. voters</div>
<div>>>>> are expected to vote so that unlisted candidates are considered "bad" and</div>
<div>>>>> listed candidates "good"; unlisted candidates are thus not just purely "tied</div>
<div>>>>> last")</div>
<div>>>>> - In elections where unlisted candidates should be considered purely</div>
<div>>>>> "tied last" Woodall's criterion is not relevant (i.e. when one wants "B" to</div>
<div>>>>> mean "B>A=C" and nothing more than that)</div>
<div>>>></div>
<div>>>> Well, I guess the relevance of any criterion depends on what the method</div>
<div>>>> is supposed to achieve.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> - There are many alternative rules for cutoffs (one could e.g. not use</div>
<div>>>>> the cutoff as a regular candidate that can win and lose to others but</div>
<div>>>>> require that n% of the votes must approve the winner)</div>
<div>>>></div>
<div>>>> Yes, I think the rule in the parentesis is the same as having a</div>
<div>>>> null-candidate, if approval is defined as explicitly ranking the cadidate on</div>
<div>>>> the ballot. As I wrote below I cannot show it though.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> </div>
<div>>>>> Thus, truncated/incomplete ballots can be completed using the</div>
<div>>>>> following generalized symmetric ballot completion algorithm, in order to</div>
<div>>>>> give same election results for margins and winning votes and to not violate</div>
<div>>>>> Woodall's plurality criterion for margins:</div>
<div>>>>> 1. add s "null candidates" under the ranked candidates, where s is the</div>
<div>>>>> number of seats</div>
<div>>>>> 2. rank the unranked candidates equally and under the "null candidate".</div>
<div>>>>> 3. equalities are resolved by giving each candidate 0.5 votes in the</div>
<div>>>>> pairwise comparison.</div>
<div>>>>> </div>
<div>>>>> If margins are used in Condorcet elections with generalized symmetric</div>
<div>>>>> ballot completion, then Woodall's plurality criterion is not violated, since</div>
<div>>>>> the "blank votes" are actually represented and the ballot is complete.</div>
<div>>>>> </div>
<div>>>>> Maybe the entry in Wikipedia could be updated, where we read "Only</div>
<div>>>>> methods employing winning votes satisfy Woodall's plurality criterion."</div>
<div>>>>> <a href="http://en.wikipedia.org/wiki/Condorcet_method#Defeat_strength">http://en.wikipedia.org/wiki/Condorcet_method#Defeat_strength</a></div>
<div>>>>> </div>
<div>>>>> I think an equality on the ballot between two candidates A=B should</div>
<div>>>>> intuitively mean nothing else than giving half a vote to A>B and B>A, i.e.</div>
<div>>>>> the pairwise comparison matrix should not change and Woodall's plurality</div>
<div>>>>> criterion should be kept at the same time. This is only possible if the</div>
<div>>>>> generalized symmetric ballot completion algorithm is used.</div>
<div>>>>></div>
<div>>>>> I think the original margins style of simply completing the ballots as</div>
<div>>>>> "tied last" without any implicit cutoff is ok and from that point of view it</div>
<div>>>>> is not a problem that it does not meet Woodall's plurality criterion (since</div>
<div>>>>> no implicit cutoff (meaning "approval" of the candidates) was intended). So</div>
<div>>>>> maybe the new method should not be considered an improved margins method but</div>
<div>>>>> as one of the approaches that have an implicit cutoff and that also meet</div>
<div>>>>> Woodall's plurality criterion.</div>
<div>>>>></div>
<div>>>>> </div>
<div>>>>> The rule of requiring the candidate to score more than 50% in a pairwise</div>
<div>>>>> comparison which I proposed in a previous email is enforced if generalized</div>
<div>>>>> symmetric completion is used.</div>
<div>>>>> </div>
<div>>>>> Furthermore, the Wikipedia entry could also mention the inclusion of</div>
<div>>>>> "null-candidates" as the natural way to enable blank voting and avoid</div>
<div>>>>> elections of candidates, where the voters would rather like to see an empty</div>
<div>>>>> seat.</div>
<div>>>>></div>
<div>>>>> Note that Wikipedia does not want to have original research. So the</div>
<div>>>>> correct approach would be to first publish the new approach somewhere and</div>
<div>>>>> only then refer to it. (Note that the electorama web site contains many new</div>
<div>>>>> proposed methods, so it can also serve as a storage place for new methods.</div>
<div>>>>> Not a wikipedia though.)</div>
<div>>>>></div>
<div>>>>> I.e., A wins the following election with current Condorcet</div>
<div>>>>> implementations (disregarding if we use margins or winning votes):</div>
<div>>>>> 45:A</div>
<div>>>>> 40:B</div>
<div>>>>> 15:Blank</div>
<div>>>>> </div>
<div>>>>> If we use generalized ballot completion, then the null-candidate wins in</div>
<div>>>>> a Condorcet election (but not in an IRV election):</div>
<div>>>>> 45:A>X>B</div>
<div>>>>> 40:B>X>A</div>
<div>>>>> 15:X>A=B</div>
<div>>>>> Woodall's plurality criterion is not violated because X is not a</div>
<div>>>>> candidate to win a seat.</div>
<div>>>>> </div>
<div>>>>> Introducing a cutoff, like saying that "a winning candidate needs to be</div>
<div>>>>> explicitly ranked on 50% of the ballots" maybe is equivalent to the</div>
<div>>>>> generalized ballot completion algorithm (I don't know). However such a</div>
<div>>>>> cutoff doesn't allow for ranking between disfavoured alternatives, which the</div>
<div>>>>> generalized ballot does.</div>
<div>>>>> </div>
<div>>>>> I aggree that it is better to require the voter to rank all candidates,</div>
<div>>>>> as an incomplete ballot is completed in any case and the voter might not</div>
<div>>>>> know the ballot completion algorithm.</div>
<div>>>>></div>
<div>>>>> Having complete rankings is good but it may be ok to accept also ballots</div>
<div>>>>> that have accidentally failed to rank some of the candidates. This depends</div>
<div>>>>> also on the number of candidates (ranking 100 of them could be too much for</div>
<div>>>>> most voters).</div>
<div>>>></div>
<div>>>> </div>
<div>>>> Well, a truncated ballot is a shorthand for a specific type of ballot. Of</div>
<div>>>> course it could be used, but the voter should know the algoritm to translate</div>
<div>>>> the shorthand to a complete ballot. But this is essentially only technical</div>
<div>>>> details. In essence, I aggree.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> </div>
<div>>>>> I don't think that introducing a null candidate in a Condorcet election</div>
<div>>>>> has any impact on its violation of Later-no-harm, i.e..the incentive of the</div>
<div>>>>> voter to bullet-vote to maximize the success of "His" candidate. Even if the</div>
<div>>>>> equalities and null candidates would be disallowed on the ballot,</div>
<div>>>>> later-no-harm would still not hold for Condorcet elections and burying would</div>
<div>>>>> still be an efficient strategy (slightly OT: the claim that Condorcet</div>
<div>>>>> methods elect centrist canidates is questionable, since the centrist</div>
<div>>>>> candidate will be the prime target for burying attempts, since he/she has</div>
<div>>>>> the highest chance of winning, thus losing his "centricity" even before it</div>
<div>>>>> is measurable in a election).</div>
<div>>>>></div>
<div>>>>> My approach to the various criteria is that one should take into account</div>
<div>>>>> also how much some method violates some criterion. No proper method meets</div>
<div>>>>> them all. Condorcet methods are very good from this point of view in the</div>
<div>>>>> sense that although they fail Later-no-harm there is "usually and by</div>
<div>>>>> default" no harm ranking also "later" candidates. Same with burial. They are</div>
<div>>>>> vulnerable to burial but "usually and by default" one need not worry about</div>
<div>>>>> burial (=not a practical strategy in typical large public elections with</div>
<div>>>>> independent voters).</div>
<div>>>></div>
<div>>>> </div>
<div>>>> OK for public elections, but for a political party, where voting strategy</div>
<div>>>> is the name of the game?</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> This "usually and by default" rule applies also e.g. to risk of one</div>
<div>>>>> party naming multiple candidates and minmax not being clone proof.</div>
<div>>>>> If people start using burial in Condorcet, I believe in most cases their</div>
<div>>>>> strategy is not a good one since using burial efficiently is so difficult.</div>
<div>>>>> Typically (I guess "usually and by default") burial attempts will just cause</div>
<div>>>>> more harm than good to the strategists.</div>
<div>>>></div>
<div>>>> </div>
<div>>>> Do you have any references for your statements concerning "usually and by</div>
<div>>>> defaults"?</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> I noted already above that having a "candidate" that can not win but</div>
<div>>>>> that can be used for burial (="X") may make burial easier and more tempting</div>
<div>>>>> than what it would be with "normal" candidates only.</div>
<div>>>></div>
<div>>>> </div>
<div>>>> Well, burial applies for complete ballots too and I think it is just as</div>
<div>>>> easy and tempting than with an added null candidate.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> </div>
<div>>>>> Thus, I think that the voter by default should be able to give a</div>
<div>>>>> partially blank vote, by completely ranking the candidates and the "null</div>
<div>>>>> candidates" using ">" and "=".</div>
<div>>>>> </div>
<div>>>>> Definition of a generalized ballot:</div>
<div>>>>> Maybe the discussion could focus more on constraints that can be put on</div>
<div>>>>> the generalized ballot, than on ballot completion algorithms.</div>
<div>>>>> </div>
<div>>>>> A generalized ballot is defined as:</div>
<div>>>>> i a partiall ordering (i.e. using only "=", ">") of the set C, where C</div>
<div>>>>> contains </div>
<div>>>>> ii. s enumerated instances of the h candidates in the election for s</div>
<div>>>>> seats: A11,..,A1s,...,Ah1,...,Ahs and</div>
<div>>>>> iii. s enumerated instances of the "null candidates" X1,...,Xs.</div>
<div>>>>></div>
<div>>>>> (I just note that there are many possible ballot formats. For example</div>
<div>>>>> one where all candidates are listed and next to them there are possible</div>
<div>>>>> ratings from 1 to 20 (to be ticked) and a clear cutoff borderline between</div>
<div>>>>> numbers 10 and 11 (=approval cutoff).)</div>
<div>>>></div>
<div>>>> </div>
<div>>>> I agree.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> </div>
<div>>>>> Some constraints on the candidate set:</div>
<div>>>>> 1. Normally we put the constraint in the election that there may only be</div>
<div>>>>> one instance of each candidate in C, i.e. C={A1,...,Ah, X1,...,Xs - each</div>
<div>>>>> elected candidate has only one seat and one vote, except for the</div>
<div>>>>> Null-candidate.</div>
<div>>>>> 2. We might restrict H in the previous point to only contain candidates</div>
<div>>>>> , i.e. C={A1,...,Ah} and no null-hopefuls, disallowing the blank vote and</div>
<div>>>>> thus requiring a complete ranking of the candidate list.</div>
<div>>>>></div>
<div>>>>> (You didn't define and discuss basic uses of multiple null candidates</div>
<div>>>>> and multi-winner elections very much.)</div>
<div>>>></div>
<div>>>> </div>
<div>>>> Basically in a multiwinner elections you have as many null-candidates as</div>
<div>>>> seats, which I think is covered by the definition above and by constraint 1</div>
<div>>>> above, as the number of instances of the null candidate equals the number of</div>
<div>>>> seats (s) in the election.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> </div>
<div>>>>> Some ideas:</div>
<div>>>>> An other interesting issue, is if election systems with several election</div>
<div>>>>> election rounds can improve results in Condorcet elections, for instance, an</div>
<div>>>>> STV Condorcet election could be held with three seats.</div>
<div>>>>> </div>
<div>>>>> Those who get one of the seat go through to the second round (which</div>
<div>>>>> maybe can be automatical), where one of the candidates is elected in a</div>
<div>>>>> Condorcet election, where a Condorcet winner is guaranteed.</div>
<div>>>>> </div>
<div>>>>> Maybe an election type could be devised which makes a bottom-up</div>
<div>>>>> proportional ranking. At the start of the election, as many seats as there</div>
<div>>>>> are candidates are elected, then in each subsequent round one candidate is</div>
<div>>>>> dropped util we have a Condorcet winner. </div>
<div>>>>> </div>
<div>>>>> Example: start with six candidates and elect five of them in a five-seat</div>
<div>>>>> Condorcet-STV election, check if we have a Condorcet winner, if not, out of</div>
<div>>>>> these five, elect four of them in a four-seat election and check if we have</div>
<div>>>>> a Condorcet winner if not elect three of them in a three-seat election. Amon</div>
<div>>>>> the three elected there is always a Condorcet winner.</div>
<div>>>>> </div>
<div>>>>> Well, it's a new method at least.Could be worth trying out, maybe it</div>
<div>>>>> will help resist burying or have some other nice properties.</div>
<div>>>>> </div>
<div>>>>> Do you or anyone else around on this list have a reference to where the</div>
<div>>>>> debate between IRV and Condorcet stands today (pros and cons of the methods</div>
<div>>>>> respectively)?</div>
<div>>>>> </div>
<div>>>>> Personally I am not yet convinced that Condorcet is a "better method"</div>
<div>>>>> than IRV when it comes to resisting tactical voting.</div>
<div>>>>></div>
<div>>>>> They are quite different methods with respect to strategic voting. To me</div>
<div>>>>> the promise of Condorcet methods is that in typical political elections they</div>
<div>>>>> may avoid (rational) strategic voting even completely.</div>
<div>>>></div>
<div>>>> </div>
<div>>>> If you mean public elections, then maybe. If you by "typical political</div>
<div>>>> elections" mean elections in a political party, then I do certainly not</div>
<div>>>> aggree.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> If there is a top level cycle, then people may afterwards think "I</div>
<div>>>>> should have voted that way", but it is not easy to know what to do (except</div>
<div>>>>> to vote sincerely) before the election.</div>
<div>>>></div>
<div>>>> </div>
<div>>>> I don't aggree. There is polling and the voter normally knows who is the</div>
<div>>>> biggest competitor to the "favored" candidate. The competitor is buried. The</div>
<div>>>> voters for the competitor bury your favorite candidate, and the winner is a</div>
<div>>>> "nobody" that no-one cared enough about to out-maneuver and noone supports,</div>
<div>>>> but also noone dislike. In a polarized environment that is not an unlikely</div>
<div>>>> scenario.</div>
<div>>>> </div>
<div>>>> I do not personally like the idea of keeping the voter "uninformed" of</div>
<div>>>> the workings of an election system and their different strategies.</div>
<div>>>> That is a path I do not want to walk.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> In IRV one may end up sooner in situations where e.g. some voter group</div>
<div>>>>> knows that it should compromise (and thereby improve the result of the</div>
<div>>>>> election). This may happen e.g. when a Condorcet winner is about to be</div>
<div>>>>> eliminated at the first round and as a result "the other side" is likely to</div>
<div>>>>> win. This example is not really on "resisting tactical voting" but on</div>
<div>>>>> "requiring tactical voting". Maybe this describes my first thoughts on this</div>
<div>>>>> topic well enough. I will not try to prove these claims here (that would</div>
<div>>>>> require too many lines of text :-). IRV had some problems at least in</div>
<div>>>>> Burlington in 2009 (the Condorcet winner was eliminated).</div>
<div>>>></div>
<div>>>> </div>
<div>>>> Well I think that IRV might be a good approach to find the two or three</div>
<div>>>> candidates to meet in the second round.</div>
<div>>>> </div>
<div>>>> When I look at the Burlington result, then what first comes to mind is</div>
<div>>>> that the winner (Bob Kiss) didn't get 50% of the votes, but only 4313 out of</div>
<div>>>> 8980 votes (48%), since there were 606 "Exhausted votes" in the final round,</div>
<div>>>> i.e. IRV used dynamic droop quotas.</div>
<div>>>> </div>
<div>>>> Thus IRV didn't respect the partially blank vote and this might be a</div>
<div>>>> reason why there is so much controversy around this election.</div>
<div>>>> A second option would have been to require complete ballots without the</div>
<div>>>> possibility to blank vote, which however might have triggered a new</div>
<div>>>> candidate "None of the Above" OR "Mr. Blank" in the election :o).</div>
<div>>>> </div>
<div>>>> So let us assume Bob Kiss wasn't elected, since he didn't get >50% of the</div>
<div>>>> votes in the end, what would have happened?</div>
<div>>>> </div>
<div>>>> Well, one approach mighet have been to hold a second round election,</div>
<div>>>> would be held, which is how presidents and such are elected most over</div>
<div>>>> Europe.</div>
<div>>>> </div>
<div>>>> In the second round either two or three candidates could meet depending</div>
<div>>>> on the favoured result (IRV or Condorcet).</div>
<div>>>> </div>
<div>>>> If there was only one round for the election, then I would have favoured</div>
<div>>>> to eliminate Bob Kiss (he got his chance, but didn't make 50%), and re-run</div>
<div>>>> the election.</div>
<div>>>> </div>
<div>>>> With Bob Kiss eliminated, Andy Montroll would have won and everyone would</div>
<div>>>> have been happy. I did a quick and dirty run on the reduced election data</div>
<div>>>> with Kiss, Wright and Montroll (<a href="http://rangevoting.org/JLburl09.txt">http://rangevoting.org/JLburl09.txt</a>, at the</div>
<div>>>> end) and Bob Kiss eliminated. Andy Montroll got more than the 4490 votes</div>
<div>>>> needed (4968 votes)</div>
<div>>>> </div>
<div>>>> Maybe a new IRV method could be considered: IRV with static quotas.</div>
<div>>>> If the IRV winner doesn't make >50%, then the IRV winner deleted and the</div>
<div>>>> IRV election is re-run.</div>
<div>>>> The generalized ballot can also be used for IRV-STV, but then we would</div>
<div>>>> have to add the rule that the null candidate(s) cannot be deleted.</div>
<div>>>> </div>
<div>>>> Ballot files used for Burlington (X are the blank ballots):</div>
<div>>>> </div>
<div>>>> With Kiss (K)</div>
<div>>>> 1332 M>K>W</div>
<div>>>> 767 M>W>K</div>
<div>>>> 455 M</div>
<div>>>> 2043 K>M>W</div>
<div>>>> 371 K>W>M</div>
<div>>>> 568 K</div>
<div>>>> 1513 W>M>K</div>
<div>>>> 495 W>K>M</div>
<div>>>> 1289 W</div>
<div>>>> 147:X</div>
<div>>>> </div>
<div>>>> Without Kiss (K):</div>
<div>>>> 1332:M>W</div>
<div>>>> 767:M>W</div>
<div>>>> 455:M</div>
<div>>>> 2043:M>W</div>
<div>>>> 371:M>W</div>
<div>>>> 568:X</div>
<div>>>> 1513:W>M</div>
<div>>>> 495:W>M</div>
<div>>>> 1289:W</div>
<div>>>> 147:X</div>
<div>>>>></div>
<div>>>>> To summarize my thoughts also after reading the mail...</div>
<div>>>>> - I like explicit cutoff marks when they carry a clear agreed message</div>
<div>>>>> that voters can easily and sincerely (not to implement a strategy) rank</div>
<div>>>>> (e..g. between acceptable and non-acceptabe candidates)</div>
<div>>>>> - Ranked ballots can thus be efficiently used for collecting also</div>
<div>>>>> additional information in addition to basic ranking data</div>
<div>>>>> - In elections where there is no clear cutoff information to be</div>
<div>>>>> collected, basic rankings will work fine (i.e. no need for fixes in the</div>
<div>>>>> basic case, it works fine as it is)</div>
<div>>>>></div>
<div>>>>> - There are many possible rules on how to take the cutoffs into account</div>
<div>>>>> in the vote counting process (check impact on strategic voting)</div>
<div>>>></div>
<div>>>> </div>
<div>>>> Yes here I am OK with you.</div>
<div>>>> </div>
<div>>>>></div>
<div>>>>> Juho</div>
<div>>>>></div>
<div>>>>></div>
<div>>>>> </div>
<div>>>>> Best regards</div>
<div>>>>> Peter Zborník</div>
<div>>>>> </div>
<div>>>>> </div>
<div>>>>> On Sun, May 29, 2011 at 4:29 PM, Juho Laatu <<a href="mailto:juho4880@yahoo.co.uk">juho4880@yahoo.co.uk</a>></div>
<div>>>>> wrote:</div>
<div>>>>> </div>
<div>>>>>></div>
<div>>>>>> On 29.5.2011, at 16.06, Peter Zbornik wrote:</div>
<div>>>>>> </div>
<div>>>>>> > On the other hand I might rather prefer "My Political Opponent" to be</div>
<div>>>>>> > elected than "Pol Pot".</div>
<div>>>>>> > Thus a ballot on the form A>X>My Political Opponent>Pol Pot, might be</div>
<div>>>>>> > a good idea to allow.</div>
<div>>>>>> </div>
<div>>>>>> </div>
<div>>>>>> I like this kind of explicit cutoffs more than implicit ones (at the</div>
<div>>>>>> end of the ranked candidates) since implicit cutoff easily encourages</div>
<div>>>>>> truncation. If people like to truncate their strongest opponents we might</div>
<div>>>>>> end up having bullet votes only. That would mean that we would be back in</div>
<div>>>>>> plurality, and all useful information of the ranked votes would be gone.</div>
<div>>>>>> </div>
<div>>>>>> The explicit cutoff works well in elections where it is possible not to</div>
<div>>>>>> elect anyone (maybe keep the old elected alternative, or maybe arrange a new</div>
<div>>>>>> election after a while). One could also have elections where there are many</div>
<div>>>>>> possible outcomes, e.g. a seat for 6 months or a seat for 2 years</div>
<div>>>>>> (A>2y>B>C>6m>D). In these cases it is possible to measure quite reliably</div>
<div>>>>>> which candidates fall into which categories (e.g. "approvable enough"). The</div>
<div>>>>>> detailed rules on how to interpret e.g. a pairwise defeat to a cutoff entity</div>
<div>>>>>> have to be agreed.</div>
<div>>>>>> </div>
<div>>>>>> Using the cutoff to give "negative votes" to candidates below the</div>
<div>>>>>> cutoff line (in the sense that such "negative votes" would really decrease</div>
<div>>>>>> their chance of winning candidates above the cutoff line) may be problematic</div>
<div>>>>>> since people could start giving negative votes to their worst competitors as</div>
<div>>>>>> a default strategy.</div>
<div>>>>>> </div>
<div>>>>>> There have been also various proposals allowing strength of preference</div>
<div>>>>>> to be expressed (e.g. A>B>>>C>D>>E).</div>
<div>>>>>> </div>
<div>>>>>> Juho</div>
<div>>>>>> </div>
<div>>>>>> </div>
<div>>>>>> </div>
<div>>>>>> </div>
<div>>>>>> ----</div>
<div>>>>>> Election-Methods mailing list - see <a href="http://electorama.com/em">http://electorama.com/em</a> for list</div>
<div>>>>>> info</div>
<div>>>>>> </div>
<div>>>>></div>
<div>>>>> </div>
<div>>>>> ----</div>
<div>>>>> Election-Methods mailing list - see <a href="http://electorama.com/em">http://electorama.com/em</a> for list</div>
<div>>>>> info</div>
<div>>>>></div>
<div>>>>></div>
<div>>>>> ----</div>
<div>>>>> Election-Methods mailing list - see <a href="http://electorama.com/em">http://electorama.com/em</a> for list</div>
<div>>>>> info</div>
<div>>>>></div>
<div>>>></div>
<div>>></div>
<div>></div>
<div>></div>
<div> </div>
<div> </div>