Dear all,<div><br></div><div>an alternative way to count wins against equally ranked candidates, </div><div>would be to give both 0.5 wins per vote and not 0 as I did in my previous mail.</div><div><br></div><div>Thus the current state: A>B gives 1:0. A=B gives ?:? (A=B is only allowed at the end of the ballot)</div>
<div>The proposal above: A>B gives 2:0. A=B gives 1:1 (linear transformation from A>B - 1:0 and A=B - 0.5:0.5).</div><div>The soccer proposal A>B gives 3:0, A=B gives 1:1 (linear transformation from A>B - 1:0 and A=B -1/3:1/3. This proposal would (as in soccer) encourage voters to differenciate between candidates, and candidates to try to gain more support than the other candidates. The soccer ranking is purely speculative though. </div>
<div><br></div><div>In the case, where we give 0.5 wins to equally-ranked candidates and 1 win to higher ranked candidates, then I guess the second example below would become:<br></div><div><div><br></div><div><span style="white-space: pre; "> </span>A<span style="white-space: pre; "> </span>B<span style="white-space: pre; "> </span>C</div>
<div>A<span style="white-space: pre; "> </span>30.5<span style="white-space: pre; "> 45</span></div><div>B<span style="white-space: pre; "> </span>31.5<span style="white-space: pre; "> 45</span></div><div>C<span style="white-space: pre; "> </span>17<span style="white-space: pre; "> </span>17<span style="white-space: pre; "> </span></div>
<div><span style="white-space: pre; "><br></span></div><div><span style="white-space: pre; ">given</span></div><div><span style="white-space: pre; "><span class="Apple-style-span" style="white-space: normal; "><div>30<span style="white-space: pre; "> </span>B>C=A</div>
<div>30<span style="white-space: pre; "> </span>A>C=B</div><div>1<span style="white-space: pre; "> </span>C (i.e. C>A=B)</div><div>1<span style="white-space: pre; "> </span>C>B>A</div><div><br></div></span></span></div>
<div><span style="white-space: pre; ">Thus B wins, but C does better than in the example below.</span></div><div><span style="white-space: pre; "><br></span></div><div><span style="white-space: pre; ">The example above is not the best illustration of how equal rankings can change election results, </span></div>
<div><span style="white-space: pre; ">since a voter can always vote B>C=A by simply bullet-voting B.</span></div><div><span style="white-space: pre; ">A better example would be on the form A=B>C or A>B=C>D, but I hope you get the point.</span></div>
<div><span style="white-space: pre; "><br></span></div><div><span style="white-space: pre; ">The question is, what the benefits and draw-backs are, if equal ranking of candidates is allowed and if equal ranking should be allowed, but discouraged, as in the soccer proposal.</span></div>
<div><span style="white-space: pre; ">If there are no draw-backs, then this ballot-type could be of use.</span></div><div><span style="white-space: pre; "><br></span></div><div><span style="white-space: pre; ">This is just a question out of curiousity and is really not a question for the green party council elections.</span></div>
<div><span class="Apple-style-span" style="white-space: pre;">I hope I haven't spammed this you too much with these emails.</span></div><div><span class="Apple-style-span" style="white-space: pre;"><br></span></div><div>
<span class="Apple-style-span" style="white-space: pre;">Best regards</span></div><div><span class="Apple-style-span" style="white-space: pre;">Peter Zborník</span></div><div><span style="white-space: pre; "><br></span></div>
</div><div><br><div class="gmail_quote">On Sun, May 9, 2010 at 2:52 PM, Peter Zbornik <span dir="ltr"><<a href="mailto:pzbornik@gmail.com">pzbornik@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div>Dear all</div><div><br></div>If we study Condorcet voting with the two types of ballots: ranked and hybrid, then the differences can be drastic:<div><div><br></div><div>Normal ranked ballots:</div><div>30<span style="white-space:pre"> </span>B>C>A</div>
<div>30<span style="white-space:pre"> </span>A>C>B</div><div>1<span style="white-space:pre"> </span>C (i.e. C>A=B, when using Schulze, see <a href="http://en.wikipedia.org/wiki/Schulze_method#Ballot" target="_blank">http://en.wikipedia.org/wiki/Schulze_method#Ballot</a>)</div>
<div>1<span style="white-space:pre"> </span>C>B>A</div><div><br></div><div>Pairwise preferences</div><div><span style="white-space:pre"> </span>A<span style="white-space:pre"> </span>B<span style="white-space:pre"> </span>C</div>
<div>A<span style="white-space:pre"> </span>30<span style="white-space:pre"> </span>30</div><div>B<span style="white-space:pre"> </span>31<span style="white-space:pre"> </span>30</div>
<div>C<span style="white-space:pre"> </span>32<span style="white-space:pre"> </span>32<span style="white-space:pre"> </span></div><div><br></div><div>Thus C wins</div>
<div><br></div><div>Hybrid ranked ballots (replace two > with = in the example above):</div><div>30<span style="white-space:pre"> </span>B>C=A</div><div>30<span style="white-space:pre"> </span>A>C=B</div>
<div>1<span style="white-space:pre"> </span>C (i.e. C>A=B)</div><div>1<span style="white-space:pre"> </span>C>B>A</div><div><br></div><div><span style="white-space:pre"> </span>A<span style="white-space:pre"> </span>B<span style="white-space:pre"> </span>C</div>
<div>A<span style="white-space:pre"> </span>30<span style="white-space:pre"> </span>30</div><div>B<span style="white-space:pre"> </span>31<span style="white-space:pre"> </span>30</div>
<div>C<span style="white-space:pre"> </span>2<span style="white-space:pre"> </span>2<span style="white-space:pre"> </span></div><div><span style="white-space:pre"><br>
</span></div><div><span style="white-space:pre">T</span>hus B wins.</div><div><br></div><div>I hope I calculated correctly.</div><div><br></div><div>As a voter, I would prefer the hybrid ballot, as it gives me more expressive power, unless this kind of ballot has some other weakness when used.</div>
<div><br></div><div>Best regards</div><div>Peter Zborník</div><div><div></div><div class="h5"><br><div class="gmail_quote">On Sun, May 9, 2010 at 2:26 PM, Peter Zbornik <span dir="ltr"><<a href="mailto:pzbornik@gmail.com" target="_blank">pzbornik@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div>Dear all,</div><div><br></div><div>have the properties of hybrid or generalized ranking/approval ballots been examined?</div>
<div>A hybrid/generalized ranking/approval ballot is a ballot, with where the voter ranks the candidates by either > or = without any other restrictions.</div>
<div>Say we have seven candidates ABCDEFG.</div><div>Say the voter likes A the most, then BC the same, then DE the same and last FG.</div><div>Then instead of having the ranking A>B>C>D>E>F>G, or some approval of ABC for instance, the ballot would look like</div>
<div>A>B=C>D=E>F=G.</div><div>For this type of ballot, the approval and ranked ballot would be a special case.</div><div>I speculate that, such a hybrid ballot might take the best of two worlds: the expressiveness of the fully ranked ballot and the robustness of the approval voting ballot.</div>
<div><br></div><div>The voters (at least I) would most likely appreciate this liberation of their preferences, since they might themselves decide to use a fully ranked ballot, an approval ballot or something inbetween.</div>
<div><br></div><div>It seems that for instance the Schulze single-winner method allows for a simplified hybrid system, as it allows for not listing all candidates.</div><div><br></div><div>Would be nice to know your thoughts on this.</div>
<div>Are hybrid ranked ballots a good idea?</div><div>Would your preferred methods be able to handle hybrid?</div><div><br></div><div>Best regards</div><div>Peter Zborník</div>
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