<HTML><BODY>
<div> From: wds@math.temple.edu<br>
> 3. Random tie-breaking is essential so all <span class="correction" id="">candiate</span> <span class="correction" id="">winnign</span> chances are always<br>
> 100% independent of the candidate-ordering.<br>
<br>
<span class="correction" id="">Definately</span>.<br>
<br>
> 4. I find <span class="correction" id="">Venzke's</span> discovery with a 10-candidate set that "<span class="correction" id="">IRV</span> tends to favor<br>
> outsiders"<br>
> whereas "Approval(mean-based cutoff) tends to favor <span class="correction" id="">centrists</span>" very interesting.<br>
> But it needs more investigation with<br>
<br>
This <span class="correction" id="">sorta</span> makes sense as <span class="correction" id="">centre</span> squeeze is a known issue of <span class="correction" id="">IRV</span><br>
<br>
> 5. Approval(mean based cutoff) looks pretty bad in these <span class="correction" id="">sims</span>, although so far<br>
> the<br>
> <span class="correction" id="">sims</span> have not employed correct random <span class="correction" id="">tiebreaking</span> so I don't know how much of<br>
> them to believe. But anyway, it would be interesting when that issue is<br>
> repaired. This seems to be the possible basis for a good attack against<br>
> Approval Voting.<br>
<br>
The new results (on Brian <span class="correction" id="">Olson's</span> site) do in fact have the random tie<br>
break rule.<br>
<br>
I think a zero info strategy is always going to have problems for approval.<br>
<br>
><br>
> 6. However, I have proved the following theorems in the large#voters limit:<br>
> (a) approval with randomized-oblivious thresholds chosen by voters yields<br>
> <span class="correction" id="">Voronoi</span> diagram.<br>
> (b) approval with the following kind of strategic voters, also yield <span class="correction" id="">Voronoi</span><br>
> diagrams:<br>
> 1. run approval election. (Say X wins.)<br>
> 2. cast votes using <span class="correction" id="">X's</span> utility as cutoff where<br>
> Y>X ==> approve Y.<br>
> Y<X ==> disapprove Y.<br>
>
Y=X ==> toss a fair coin to decide to approve or
disapprove Y.<br>
> 3. go back to (1) until stabilizes on a single winner who keeps winning.<br>
> which two theorems, I suppose, form some sort of defense for approval voting.<br>
<br>
This means that the winner of the previous election has a 50% chance of being<br>
approved by each voter, so only the <span class="correction" id="">condorcet</span> winner can be stable ?<br>
<br>
><br>
> 7. Why the heck are you simulators not trying RANGE VOTING? (With voters<br>
> who "normalize" their range scores x via x --> (<span class="correction" id="">x-worstScore</span>)/(<span class="correction" id="">bestScore-worstScore</span>)<br>
> so that the best candidate gets range vote 1, the worst 0, and the rest are<br>
> <span class="correction" id="">reals</span><br>
> somewhere in between? [<span class="correction" id="">Bolson</span> actually had "range voting" = "social utility<br>
> winner"<br>
> computing twice the same thing with different names, which was both false and<br>
> silly.]<br>
<br>
Yeah, I said the same thing.<br>
<br>
The source is available to add new methods.<br>
<br>
</div>
<div> </div>
<div style="clear: both;"><span class="correction" id="">Raphfrk</span><br>
--------------------<br>
Interesting site<br>
"what if anyone could modify the laws"<br>
<br>
<span class="correction" id="">www</span>.<span class="correction" id="">wikocracy</span>.<span class="correction" id="">com</span></div>
<div> </div>
<br>
<br>
<!-- end of AOLMsgPart_0_3fb1ec37-f49a-449a-a89b-15622f8a2195 -->
<div class="AOLPromoFooter">
<hr style="margin-top:10px;" />
<a href="http://pr.atwola.com/promoclk/100122638x1081283466x1074645346/aol?redir=http%3A%2F%2Fwww%2Eaim%2Ecom%2Ffun%2Fmail%2F" target="_blank"><b>Check Out the new free AIM(R) Mail</b></a> -- 2 GB of storage and industry-leading spam and email virus protection.<br />
</div>
</BODY></HTML>