<div dir="ltr"><p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Esteemed gentlemen of the EM list, </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Among the risks inherent in following some of the
discussion here for some time is that one is apt to start to tinker with rules
on their own. Having done so, one is then apt to present his thinking to the EM
list to humbly ask whether one has reinvented the wheel or, if not, if the
method proposed has any merit. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">The idea is to strike some balance between latter-no-harm
and favorite betrayal, perhaps not meeting either but practically meeting both
to a good degree, by mimicking how a reasonable voter would vote given some
(but not full) knowledge of the situation. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">The method is a variation of Bucklin where the algorithm
used to progress into the next round is different. Voters present ranked
ballots, truncation and equal ranking allowed. As in Bucklin, majority of first
preferences (but only of first preferences) ends the race. If no candidate has
such majority, the count proceeds in rounds where each ballot reveals N of
their top preferences as follows: </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">- at any point, the placeholder winner (candidate(s) with
most approvals so far) is revealed </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">- whoever has not approved of the placeholder winner yet,
reveals one more preference </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">- whoever has approved of the placeholder winner and no
candidate further below, is stationary </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">- whoever has approved of the placeholder winner and some
candidates further below, reverts back to revealing only as far down their vote
as the placeholder winner </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">All “moves” are run concurrently in simulated ignorance of other voters’ moves, all in discrete rounds. When no more moves are
possible (all ballots are either exhausted or go as far down in their
preferences as the placeholder winner) the placeholder winner is elected. The
rules change, mutatis mutandis, where there are two or more placeholder winners
at any given round (reveal only your favorite among them, keep going if you
approve of neither so far). </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Has something of the sort (or similar enough) been proposed
yet to your knowledge? If not, would this indeed meet the design criteria of a
compromise between LNH and FB? </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Thank you for your time, </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Etjon Basha </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">EXAMPLE 1: </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">9 voters and 4 candidates, 3 ABC, 2 BDC, 2 CDA </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">First round: 3 A, 2 B, 2 C. No candidate has majority,
count continues, A in placeholder winner (PW) with 3 approvals. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Second round: 3 A (approves of PW so no more preferences
revealed), 2 BD (reveals one more), 2 CD (reveals one more). D becomes PW with
4 approvals. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Third round: 3 AB (reveals one more), 2 BD and 2 CD (both
approve of PW so no more preferences revealed). B becomes PW with 5 approvals. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Fourth round: 3 AB, 2 B (approves one more than PW, so goes
back to revealing only PW), 2 CDA (reveals one more). A and B become PWs with 5
approvals each. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Fifth round: 3 A (approves one more than their preferred
PW, so goes back to revealing only preferred PW), 2B (no change), 2 CDA (no
change). A becomes PW with 5 approvals. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Sixth round: 3 A, 2 BD (reveals one more), 2 CDA. A still
PW with 5 approvals. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Seventh round: 3 A, 2 BDC, 2 CDA. No more moves possible,
current placeholder winner A is elected with 5 approvals. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">In this (admittedly convoluted) example A wins but standard
Bucklin would have elected B in round to with 5 approvals, due to A’s votes
helping B at A’s expense. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">EXAMPLE 2: </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Taken from Warren D. Smith’s February 2014 example of
Condorcet contradiction (<a href="https://rangevoting.org/CondCoursera.html" style="color:rgb(5,99,193)">https://rangevoting.org/CondCoursera.html</a>) </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">100 voters, 3 candidates: 35 ABC, 21 BAC, 21 BCA, 21 CAB, 1
ACB, 1 CBA. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:106%;font-size:11pt;font-family:Calibri,sans-serif"><span style="color:black">Not going through the process, the method elects B in 3
rounds, while the Condorcet winner is A (incidentally showing this method does
not meet Condorcet). In this case, standard Bucklin would have also elected
B. </span></p></div>