<div dir="ltr">The Droop quota is often presumed for proportional representation<div>over the Hare quota that is more proportional, due to how the Hare quota</div><div>can result in a minority being in power. (I guess the majority get in power only a</div>
<div>majority of the time with a Hare Quota. )<br><div>And since the amount of proportionality with a droop quota</div><div> gets watered down as the number of contested seats is reduced, this has led </div><div style>some activists/experts, like Douglas Amy, to insist that PR use at least 5 seats.</div>
<div style>This is often coupled with an insistence on rank choice voting due to the problems with party lists. <br></div><div style><br></div><div style>So I'd like to simulate the effects of using 3-seat LR Hare for a 13 seat city council election, like in MInneapolis, MN. </div>
<div style><br></div><div style>We'd consider 7 cases:</div><div style>1. 13 FPTP elections.</div><div style>2. 13 IRV elections, as are used now. </div><div style>3. Four 3-seat LR Hare elections with 1 at-large seat with IRV.</div>
<div style>4. A 6 and a 7 seat with Droop quota election.</div><div style>5. A 6 and a 7 seat with Hare quota election.</div><div style>6. A 13 seat with Droop quota election.</div><div style>7. A 13 seat with Hare quota election.</div>
<div style><br></div><div style>I'd like to measure relative proportionality and the probability of a majority getting a ruling majority, the portion of close/competitive elections, and maybe some other stuff that cd be of interest.</div>
<div><div class="gmail_extra"><br></div><div class="gmail_extra">Anybody interested? </div><div class="gmail_extra"><br></div><div class="gmail_extra">My intuition is that smaller-order PRs retain the constituent-legislator relationship and would be preferred by many who like having their council-person. I also think that the Hare quota is more important for increasing the likelihood of having a competitive election and giving minority groups a higher chance of being swing voters. If this is paired with the use of an at-large seat or some other way of establishing a hierarchy who can get things done, it might be a winning combination.<br clear="all">
<div><div dir="ltr">dlw</div></div>
<br><br><div class="gmail_quote">On Wed, May 15, 2013 at 2:02 PM, <span dir="ltr"><<a href="mailto:election-methods-request@lists.electorama.com" target="_blank">election-methods-request@lists.electorama.com</a>></span> wrote:<br>
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Today's Topics:<br>
<br>
1. My cycle definition of the Schwartz set was incorrect<br>
(Michael Ossipoff)<br>
<br>
<br>
----------------------------------------------------------------------<br>
<br>
Message: 1<br>
Date: Tue, 14 May 2013 16:18:25 -0400<br>
From: Michael Ossipoff <<a href="mailto:email9648742@gmail.com">email9648742@gmail.com</a>><br>
To: <a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a><br>
Subject: [EM] My cycle definition of the Schwartz set was incorrect<br>
Message-ID:<br>
<CAOKDY5Dv9vjoYwO=tXpgfjh=<a href="mailto:CgG73XjPr5_7W6bLkYZ95D4ayQ@mail.gmail.com">CgG73XjPr5_7W6bLkYZ95D4ayQ@mail.gmail.com</a>><br>
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<br>
I wanted to express the beatpath definition of the Schwartz set in a<br>
simpler and more compelling or appealing way, and the cycle definition<br>
(that I've posted here) seemed such a simplification.<br>
<br>
But the cycle definition doesn't define the Schwartz set. A candidate<br>
that doesn't have a defeat that isn't in a cycle isn't necessarily in<br>
the Scwhartz set (as defined by the unbeaten set definition and the<br>
beatpath definition].<br>
<br>
Of the two definitions (unbeaten set and beatpath), the beatpath<br>
definition desn't have much compellingness. For compellingness, I much<br>
prefer the unbeaten set definition.<br>
<br>
Let me state both definitions here:<br>
<br>
Unbeaten set definition of the Schwartz set::<br>
<br>
1. An unbeaten sets is a set of alternatives none of which are beaten<br>
by anything outside the set.<br>
<br>
2. An innermost unbeaten set is an unbeaten set that doesn't contain a<br>
smaller unbeaten set.<br>
<br>
3.The Schwartz set is the set of alternatives that are in innermost<br>
unbeaten sets.<br>
<br>
[end of unbeaten set definition of Schwartz set]<br>
<br>
---------------------------------------<br>
<br>
Beatpath definition of Schwartz set:<br>
<br>
There is a beatpath from X to Y if X beats Y, or if X beats A and<br>
there is a beatpath from A to Y.<br>
<br>
If there is a beatpath from Y to X, but not from X to Y, then X is not<br>
in the Schwartz set.<br>
<br>
Otherwise X is in the Schwartz set.<br>
<br>
[end of beatpath definition of the Schwartz set]<br>
<br>
Michael Ossipoff<br>
<br>
<br>
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End of Election-Methods Digest, Vol 107, Issue 9<br>
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</blockquote></div><br></div></div></div></div>