<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 class="Apple-tab-span" style="white-space:pre"> </span>B>C>A</div>
<div>30<span class="Apple-tab-span" style="white-space:pre"> </span>A>C>B</div><div>1<span class="Apple-tab-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">http://en.wikipedia.org/wiki/Schulze_method#Ballot</a>)</div>
<div>1<span class="Apple-tab-span" style="white-space:pre"> </span>C>B>A</div><div><br></div><div>Pairwise preferences</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>A<span class="Apple-tab-span" style="white-space:pre"> </span>B<span class="Apple-tab-span" style="white-space:pre"> </span>C</div>
<div>A<span class="Apple-tab-span" style="white-space:pre"> </span>30<span class="Apple-tab-span" style="white-space:pre"> </span>30</div><div>B<span class="Apple-tab-span" style="white-space:pre"> </span>31<span class="Apple-tab-span" style="white-space:pre"> </span>30</div>
<div>C<span class="Apple-tab-span" style="white-space:pre"> </span>32<span class="Apple-tab-span" style="white-space:pre"> </span>32<span class="Apple-tab-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 class="Apple-tab-span" style="white-space:pre"> </span>B>C=A</div><div>30<span class="Apple-tab-span" style="white-space:pre"> </span>A>C=B</div>
<div>1<span class="Apple-tab-span" style="white-space:pre"> </span>C (i.e. C>A=B)</div><div>1<span class="Apple-tab-span" style="white-space:pre"> </span>C>B>A</div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>A<span class="Apple-tab-span" style="white-space:pre"> </span>B<span class="Apple-tab-span" style="white-space:pre"> </span>C</div>
<div>A<span class="Apple-tab-span" style="white-space:pre"> </span>30<span class="Apple-tab-span" style="white-space:pre"> </span>30</div><div>B<span class="Apple-tab-span" style="white-space:pre"> </span>31<span class="Apple-tab-span" style="white-space:pre"> </span>30</div>
<div>C<span class="Apple-tab-span" style="white-space:pre"> </span>2<span class="Apple-tab-span" style="white-space:pre"> </span>2<span class="Apple-tab-span" style="white-space:pre"> </span></div><div><span class="Apple-tab-span" style="white-space:pre"><br>
</span></div><div><span class="Apple-tab-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><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">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>
</blockquote></div><br></div>