<div dir="auto">Hi,<div dir="auto"><br></div><div dir="auto">This kinda reminds me of the Bayesian Truth Serum:</div><div dir="auto"><br></div><div dir="auto"><a href="https://wesselb.github.io/assets/talks/serum.pdf">https://wesselb.github.io/assets/talks/serum.pdf</a><br></div><div dir="auto"><br></div><div dir="auto"><a href="https://www.dropbox.com/s/dl/k8rdnbql1t0byxy/serum.pdf">https://www.dropbox.com/s/dl/k8rdnbql1t0byxy/serum.pdf</a></div><div dir="auto"><br></div><div dir="auto">Kind regards,</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto">Arthur</div><div dir="auto"><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, 26 Jun 2019, 20:11 Forest Simmons, <<a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>Here's the simplest version of PJ:</div><div><br></div><div>Voters submit approval ballots with favorite identified, and with a number between zero and 100 percent as their estimate of what degree of consensus is reasonably possible, the consensus potential estimate (CPE)<br></div><div><br></div><div>After the approvals have been tallied, a ballot is drawn at random.</div><div><br></div><div>If the approval winner's approval percentage is greater than both the median of all the consensus potential estimates, as well as the CPE on the drawn ballot, then the approval winner is elected.</div><div><br></div><div>Otherwise the ballot favorite is elected.<br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Jun 22, 2019 at 4:23 PM Forest Simmons <<a href="mailto:fsimmons@pcc.edu" target="_blank" rel="noreferrer">fsimmons@pcc.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>PJ stands for either Proportional Judgment (as opposed to Majority Judgment) or Poetic Justice (see if you agree).</div><div><br></div><div>Voters submit approval ballots along with a circled favorite and a number R between zero and one that the voter of the ballot thinks is a good approval score given the chances for consensus. <br></div><div><br></div><div>Let P (between zero and one) be the average approval of the approval winner. Let Q (between zero and one) be the median of the submitted numbers.</div><div><br></div><div>A ballot B is drawn. Let R be the reasonable number marked on the ballot, and let F be the indicated favorite.<br></div><div><br></div><div>If R>P, then elect the favorite or the approval winner with probabilities R and (1-R) respectively.</div><div><br></div><div>[Note that if R=P=1, the favorite must be the same as the approval winner.]<br></div><div><br></div><div>Otherwise (If R is no greater than P) ...</div><div>... If P is in the closed interval [Q, 1], then elect the approval winner</div><div>.... else defer the decision to a second randomly drawn ballot. <br></div><div><br></div><div>I admit there is room for tweaking, but my main idea is to give incentive for the max possible consensus. <br></div><div><br></div><div>The interesting case is when R is less than both P and Q. In this case both according to the voter of the random ballot and the median estimate of reasonable possible consensus, the approval has fallen short of its potential, so random favorite, the fall back benchmark, should be invoked. Hence the second random ballot in this case. <br></div><div><br></div><div>Does the whole process start over again with the second randomly drawn ballot? Possibly, but let's keep it simple. Just take the favorite of the second ballot.<br></div><div><br></div><div>Why not just use F from the first random ballot in this case, with probabilitty R, and revert to a second random ballot with probability (1-R). That is another possibility. And I'm sure there are other acceptable or even better ways to use the values of R, P, Q, and F to decide what to do.</div><div><br></div><div>I appreciate your thoughts.</div><div><br></div><div>Forest<br></div></div>
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