<div dir="auto"><div>I forgot to mention that Gross Loser Elimination is just as burial resistant and Chicken resistant as IRV, and is less susceptible to compromise than IRV, because unlike IRV, it has no Central Squeeze pathology.</div><div dir="auto"><br></div><div dir="auto">Imagine candidates X and Y close to the left and right of Center Z. Under sincere ranked ballots Z will have few first choice votes compared to X and Y, so it will be eliminated, unless one of the factions compromises and votes its second choice Z over its favorite.</div><div dir="auto"><br></div><div dir="auto">Which one would benefit by that insincere order reversal?</div><div dir="auto"><br></div><div dir="auto">Answer: the pairwise loser in the final runoff step between X and Y.</div><div dir="auto"><br></div><div dir="auto">A note on counting GLE.... a rectangular table of pairwise counts is projected on the screen in the public counting room.</div><div dir="auto"><br></div><div dir="auto">The k_th entry in the j_th row of the table is the number of ballots on which the j_th candidate out ranks the k_th candidate. </div><div dir="auto"><br></div><div dir="auto">As the ballots are opened and the candidate rankings carefully compared one-by-one, the respective table entries for row j are incremental for each candidate k that candidate j outranks on that ballot.</div><div dir="auto"><br></div><div dir="auto">When the ballots have been fully tabulated, the elimination steps begin.</div><div dir="auto"><br></div><div dir="auto">At each step the smallest entry in the table is circled. All viewers must agree that it is indeed the smallest entry before continuing the step. </div><div dir="auto"><br></div><div dir="auto">Once all observers are in agreement that the smallest entry is the k_th entry of row j, then candidate j is declared to be the Gross Loser of this step, and so is eliminated by crossing out both the j_th row and the j_th column of the table.</div><div dir="auto"><br></div><div dir="auto">The remaining table has one fewer row and one fewer column.</div><div dir="auto"><br></div><div dir="auto">Find the Gross Loser of this smaller table by identifying which row has the smallest entry, etc.</div><div dir="auto"><br></div><div dir="auto">The last candidate standing is the GLE winner.</div><div dir="auto"><br></div><div dir="auto">If you want the frosting on the cake, have a representative for each candidate announce if they claim to have the highest uncovered candidate in the finish order.</div><div dir="auto"><br></div><div dir="auto">Process these claims in the reverse order, beginning with the GLE winner, then the runner up, etc until either a claim is verified, or all have been checked and refuted.</div><div dir="auto"><br></div><div dir="auto">To check a claim X, those who challenge X must produce a candidate Y who beats X, but is not at the end of a two step beat path from X to Y.</div><div dir="auto"><br></div><div dir="auto">If the challengers cannot successfully refute the claim in this manner, then the claim stands approved, and X is the winner.</div><div dir="auto"><br></div><div dir="auto">In other words, elect the candidate with the first unrefutted claim in the order of claim processing ... which (as we have already specified) is the reverse of the elimination order.</div><div dir="auto"><br></div><div dir="auto">Anybody have a better suggestion?</div><div dir="auto"><br></div><div dir="auto">Nobody?</div><div dir="auto"><br></div><div dir="auto"><span style="font-family:sans-serif">OK, then...how do we get the proposal ball rolling?</span><br></div><div dir="auto"><br></div><div dir="auto">-Forest</div><div dir="auto"><br></div><div dir="auto"><br><div class="gmail_quote" dir="auto"><div dir="ltr" class="gmail_attr">On Wed, Nov 9, 2022, 8:50 AM Forest Simmons <<a href="mailto:forest.simmons21@gmail.com">forest.simmons21@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto">This same simple tweak works on any method with a built in finish order, including any one-at-a-time elimination method like IRV, BTR-IRV, Baldwin, etc:<div dir="auto"><br></div><div dir="auto">Elect the uncovered candidate highest in the finish order.</div><div dir="auto"><br></div><div dir="auto"><div dir="auto" style="font-family:sans-serif">Why does our suggested tweak say to elect the highest uncovered candidate in the finish order, instead of the highest unbeaten candidate in the finish order?</div><div dir="auto" style="font-family:sans-serif"><br></div><div dir="auto" style="font-family:sans-serif">Answer: because sometimes there is no unbeaten candidate, but there is always an uncovered candidate.</div></div><div dir="auto"><br></div><div dir="auto">The simplest and best one-by-one elimination method is Gross Loser Elimination.</div><div dir="auto"><br></div><div dir="auto">No other one-at-time elimination method can improve on it, much less the uncovered version:</div><div dir="auto"><br></div><div dir="auto">Elect the uncovered candidate highest in the Gross Elimination finish order.</div><div dir="auto"><br></div><div dir="auto">Like IRV it is clone free. Unlike IRV it is precinct summable on one pass through the ballots at each precinct.</div><div dir="auto"><br></div><div dir="auto">Wouldn't that have been nice last night at the midterm election count?</div><div dir="auto"><br></div><div dir="auto">Like IRV it is non monotonic, but unlike IRV it is Yee/Bolson monotonic: the win regions are convex, not pathological fractals. [I almost wrote Bolsonaro instead of Bolson ... sorry Brian!]</div><div dir="auto"><br></div><div dir="auto">Pick any method X, and pair it with Gross Loser Elimination ... uncovered version or not ... and do a pairwise runoff between the two winners.</div><div dir="auto"><br></div><div dir="auto">Not only will Gross Loser Elimination almost always come out ahead, the people who do the experiment will come away saying, "Why do we even bother with method X? GLE is so much more simple and effective." </div><div dir="auto"><br></div><div dir="auto">GLE is already Smith efficient without the uncovered tweak ... that's just optional frosting on the cake.</div><div dir="auto"><br></div><div dir="auto">It is the simplest Smith efficient method that does not require computing pairwise wins or losses. No need to mention Smith or Condorcet or pairwise defeats.</div><div dir="auto"><br></div><div dir="auto">It automatically eliminates the Condorcet Loser at any stage when there is one, because when there is a Condorcet Loser, it will also be the Gross Loser.</div><div dir="auto"><br></div><div dir="auto">The Gross Loser is the candidate with the fewest ballots preferring it over any other candidate. In a tournament, it is the candidate with the single most embarrassingly low score.</div><div dir="auto"><br></div><div dir="auto">In fact, unlike IRV, Gross Loser Elimination can be used to get a finish order for a Round Robin Tournament, so the uncovered tweak can be applied to it if so desired.</div><div dir="auto"><br></div><div dir="auto">Suppose when there are only three uneliminated teams, team Rock's scores against the other two teams stand at 60 and 40, while team Paper's scores are 45 points against one team, and 72 against the other, and finally team Scissors' scores stand at 35 and 90.</div><div dir="auto"><br></div><div dir="auto">Which team will be eliminated at this stage of GLE? </div><div dir="auto"><br></div><div dir="auto">Answer ... Scissors, because no other team scored as low as 35. </div><div dir="auto"><br></div><div dir="auto">Note that we did not even need to know who the other team was that skunked Scissors, or how much it scored in that game to know that Scissors was the Gross Loser of that round.</div><div dir="auto"><br></div><div dir="auto">Now tell me, who was the IRV loser of that round?</div><div dir="auto"><br></div><div dir="auto">Answer: impossible to know, because IRV makes no sense in a tournament context, unless it is a superficial popularity contest of some kind.</div><div dir="auto"><br></div><div dir="auto">Is this the best RCV public proposal?</div><div dir="auto"><br></div><div dir="auto">No other Universal Domain method this simple is anywhere near as good.</div><div dir="auto"><br></div><div dir="auto">How about outside the UD? Do you think STAR is a better proposal? If so why?</div><div dir="auto"><br></div><div dir="auto">-Forest</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Nov 9, 2022, 12:05 AM Forest Simmons <<a href="mailto:forest.simmons21@gmail.com" target="_blank" rel="noreferrer">forest.simmons21@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto">In this context the most relevant question is what do we mean by "uncovered", since that's the word used in the method definition ...<div dir="auto"><br></div><div dir="auto">Repeatedly eliminate the (remaining) candidate with fewest votes until there remains only one uncovered candidate to elect.</div><div dir="auto"><br></div><div dir="auto">No need to know what covering means, although you can figure it out indirectly from the definition of "uncovered:"</div><div dir="auto"><br></div><div dir="auto">A candidate is uncovered iff it has a beatpath of only two steps to each candidate (if any) that beats it.</div><div dir="auto"><br></div><div dir="auto">Any candidate X who complains that they should have won because they beat the winner W pairwise will get this truthful and obviously relevant rejoinder:</div><div dir="auto"><br></div><div dir="auto">When you were eliminated, you had fewer transferred votes than I.</div><div dir="auto"><br></div><div dir="auto">I fact, I beat every candidate pairwise that was not already eliminated (like you) on the basis of two few (transferred) votes.</div><div dir="auto"><br></div><div dir="auto">It is very easy to discern if some candidate X is uncovered:</div><div dir="auto"><br></div><div dir="auto">Just check each candidate Y that beats it (X) to see if it has a two step beatpath via some Z, back to Y:</div><div dir="auto"><br></div><div dir="auto">X beats Z beats Y </div><div dir="auto"><br></div><div dir="auto">Only Smith candidates can be uncovered because only Smith candidates have beatpaths back to the candidates that beat them. So the candidates you have to check are the Smith candidates ... at most three, and rarely more than one, in a public election.</div><div dir="auto"><br></div><div dir="auto">If you want, you can run IRV all the way through ... then if the IRV winner is uncovered, you are done. If not, back up until you cone to an uncovered candidate ... that's your winner!</div><div dir="auto"><br></div><div dir="auto">It's just a matter of doing regular IRV, and backing up (if necessary) until you get to an uncovered candidate.</div><div dir="auto"><br></div><div dir="auto">Forest</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Nov 8, 2022, 11:18 AM Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de" rel="noreferrer noreferrer noreferrer" target="_blank">km_elmet@t-online.de</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">On 08.11.2022 18:02, Richard, the VoteFair guy wrote:<br>
> Forest, what do you mean by "covered"? Is there a Wikipedia or <br>
> Electowiki article (or section of an article) that explains it? Or is <br>
> there a dictionary reference you can point to?<br>
> <br>
> Yes, you've used the words "covered" and "uncovered" many times but I <br>
> don't recall ever seeing a clear explanation of what you mean. I <br>
> presume it involves pairwise counts, but that's as far as I can guess.<br>
<br>
The short answer is: A covers B if A pairwise beats everybody B pairwise <br>
beats and then some.<br>
<br>
An uncovered candidate is someone who is not covered by anyone else.<br>
<br>
This definition works when there are no pairwise ties. Things get <br>
trickier with pairwise ties, as I found out when generalizing Friendly <br>
Cover.<br>
<br>
-km<br>
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