<div dir="auto">I tried to state the most understandable description possible of Gross Loser Elimination ... is the following version an improvement? Anybody have a simpler or clearer description?<div dir="auto"><div dir="auto"><br></div><div dir="auto">Suppose there are seven candidates. Each candidate gets six cards with their name at the top and one of the other candidate names just below it.</div><div dir="auto"><br></div><div dir="auto">Each card is given to a different election worker.</div><div dir="auto"><br></div><div dir="auto">Pretend you are in charge of the card with Diane at the top and Jenny just below it.</div><div dir="auto"><br></div><div dir="auto">As the ballots are slowly opened one by one in a public ceremony so that everybody can see each ballot on an overhead projector screen, you put a hash mark on your Diane/Jenny card every time a ballot is opened that shows a vote for Diane over Jenny.</div><div dir="auto"><br></div><div dir="auto">After the ballots have been tallied in this way, you total the votes, and put that vote total to the left of her name on the top left of your card. This is the total of her votes in her matchup against one of the other candidates, namely Jenny.</div><div dir="auto"><br></div><div dir="auto">Then you hand in your card to the head vote counter, who sorts the cards in order of the vote totals in the upper left corner of each card.</div><div dir="auto"><br></div><div dir="auto">Now the Elimination steps:</div><div dir="auto"><br></div><div dir="auto">Remove the card from the bottom of the stack, the one with the smallest vote total next to the name at the top of that card. That name identifies the Gross Loser. Eliminate all of the cards that have that name anywhere on it. That concludes one step of GLE, Gross Loser Elimination.</div><div dir="auto"><br></div><div dir="auto">Now remove the card from the bottom of the remaining deck. <span style="font-family:sans-serif">The name at the top of that card is the Gross Loser name for this step.. Eliminate all of the cards that have that name anywhere on it. That concludes another step of GLE, Gross Loser Elimination.</span></div><div dir="auto"><span style="font-family:sans-serif"><br></span></div><div dir="auto"><span style="font-family:sans-serif">Now remove the card from the bottom of the remaining deck. </span><span style="font-family:sans-serif">The name at the top of that card is the Gross Loser name for this step.. Eliminate all of the cards that have that name anywhere on it. That concludes another step of GLE, Gross Loser Elimination.</span><span style="font-family:sans-serif"><br></span></div><div dir="auto"><span style="font-family:sans-serif"><br></span></div><div dir="auto"><font face="sans-serif">Continue in this manner until all cards but two have been eliminated. Eliminate the bottom of these two, and elect the candidate whose name is at the top of the remaining card. This is the only candidate that was never at any stage the worst of the worst ... i.e. never the Gross Loser.</font></div><div dir="auto"><font face="sans-serif"><br></font></div><div dir="auto"><font face="sans-serif">-Forest</font></div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Nov 12, 2022, 12:13 PM 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"><div>Q&D was the simplest way to always get the same result (when the Smith set was four or fewer members) as Implicit Approval Chain Climbing ... a monotonic, clone free, burial resistant, Banks efficient method ... as simple as possible for a method with those criteria compliances .... compliances that no other method on record could truthfully claim.</div><div dir="auto"><br></div><div dir="auto">So why did it get no traction?</div><div dir="auto"><br></div><div dir="auto">According guys "in the trenches" it has to be an elimination method with vote transfers between steps.</div><div dir="auto"><br></div><div dir="auto">No such method is monotonic, but the next best thing is Yee/Bolson monotonic.</div><div dir="auto"><br></div><div dir="auto">That method is Gross Loser Elimination (GLE).</div><div dir="auto"><br></div><div dir="auto">The Gross Loser of a Round Robin tournament is the player whose worst score (for any of her matchups) is worse than anybody elses's ... we could call her the MinMin loser.</div><div dir="auto"><br></div><div dir="auto">GLM is the elimination method that at each stage eliminates the gross loser of the remaing candidates ... after the gross losers from the previous stages have already been removed. The last candidate standing is the winner.</div><div dir="auto"><br></div><div dir="auto">As a reminder, the gross loser is the candidate with the worst worst score. Each candidate has several scores ... one against each of the other players. The worst of these is that candidate's worst score. The candidate whose worst score is worse than anybody elses's worst score is the gross loser. That is the one to be eliminated in the first step.</div><div dir="auto"><br></div><div dir="auto">In the second step each candidate has a worst score in any of its matchups with the remaining candidates. The candidate whose worst score is worse than any other remaining candidate's worst score is the gross loser of that stage. That's the one to be eliminated at that stage.</div><div dir="auto"><br></div><div dir="auto">For example suppose that in 10th stage there are only four candidates left ... candidates A B,C,&D with respective worst matchup scores of 15, 13, 28, and 35. Which one do you think would be eliminated at that stage?</div><div dir="auto"><br></div><div dir="auto">If you guessed candidate B, you guessed right: B's worst score (13) at this stage is worse (smaller than) any of the other three scores 15, 28, or 35.</div><div dir="auto"><br></div><div dir="auto">Each elimination step is that simple!</div><div dir="auto"><br></div><div dir="auto">Where do the matchup scores come from? In a sports tournament it is obvious because each matchup is a completion for points.</div><div dir="auto"><br></div><div dir="auto">In an election each matchup is also a competition for points ... in the form of ........ (you guessed it) votes!</div><div dir="auto"><br></div><div dir="auto">The scores we've been talking about are the votes in the head-to-head matchups.</div><div dir="auto"><br></div><div dir="auto">The beauty of RCV ballots is that for each matchup you can figure out the scores for both candidates from the RCV ballots. </div><div dir="auto"><br></div><div dir="auto">Suppose the matchup in question is between candidates X and Y. </div><div dir="auto">Separate the ballots into three stacks. </div><div dir="auto"><br></div><div dir="auto">Pretend that all of the other candidates are out of the picture so that all votes are transferred to X and Y. How many votes would X get? That is X's score for this matchup.</div><div dir="auto"><br></div><div dir="auto">You don't have to actually deface the ballots by crossing out the irrelevant candidates to find X's vote totals. Just count the number of ballots on which candidate X outranks candidate Y.</div><div dir="auto"><br></div><div dir="auto">This can be done for each of X's matchups, giving a complete set of matchup scores for X.</div><div dir="auto"><br></div><div dir="auto">Similarly we can get a completes set of matchup scores for each of the other candidates.</div><div dir="auto"><br></div><div dir="auto">And the one whose worst score is worse than anybody elses's worst score is the Gross Loser.</div><div dir="auto"><br></div><div dir="auto">So, to recap the method ... in the very first step eliminate the Gross Loser. In the next step eliminate the Gross Loser from among the remaining candidates, those who were not eliminated in the first step. </div><div dir="auto"><br></div><div dir="auto">In all subsequent steps where more than two candidates remain, eliminate the Gross Loser from among those remaining candidates. </div><div dir="auto"><br></div><div dir="auto">When it gets down to two candidates eliminate the Gross Loser, the one with the lowest score, i.e. the one with the fewest votes, i.e. elect the one with the most votes in this final matchup.</div><div dir="auto"><br></div><div dir="auto">This spells it out as plainly as I can do in the abstract. But what we all know is children do not learn how to play a game by reading the instructions on the inside cover of the box. They learn by playing with friends who already know the rules.</div><div dir="auto"><br></div><div dir="auto">This little card game (ballot counting game) is much simpler than Monopoly, Poker, Uno, Clue, etc that kids feel pretty confident with after a couple of dry runs with their friends.</div><div dir="auto"><br></div><div dir="auto">A YouTube video is the second best way to teach it.</div><div dir="auto"><br></div><div dir="auto">An EM text message is the worst way to teach it ... but you guys pick things up faster than average!</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><br><div class="gmail_quote" dir="auto"><div dir="ltr" class="gmail_attr">On Thu, Nov 10, 2022, 9:07 AM Toby Pereira <<a href="mailto:tdp201b@yahoo.co.uk" target="_blank" rel="noreferrer">tdp201b@yahoo.co.uk</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div style="font-family:Helvetica Neue,Helvetica,Arial,sans-serif;font-size:13px"><div></div>
<div dir="ltr">So do you have a nice and simple definition of this method that anyone can understand?</div><div dir="ltr"><br></div><div dir="ltr">Where do you now stand on your Quick and Clean Burial Resistant Smith method? At the time, it seemed to be the best thing since sliced bread, but amongst all the posts, it now it appears not to have resisted, er, burial.</div><div dir="ltr"><br></div><div dir="ltr">Toby</div><div><br></div>
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On Wednesday, 9 November 2022 at 22:07:53 GMT, Forest Simmons <<a href="mailto:forest.simmons21@gmail.com" rel="noreferrer noreferrer" target="_blank">forest.simmons21@gmail.com</a>> wrote:
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<div><div id="m_-4340217900081642727m_-8413402865815949567ydpbe4f5970yiv4345286073"><div><div><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><br clear="none"></div><div>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><br clear="none"></div><div>Which one would benefit by that insincere order reversal?</div><div><br clear="none"></div><div>Answer: the pairwise loser in the final runoff step between X and Y.</div><div><br clear="none"></div><div>A note on counting GLE.... a rectangular table of pairwise counts is projected on the screen in the public counting room.</div><div><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>When the ballots have been fully tabulated, the elimination steps begin.</div><div><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>The remaining table has one fewer row and one fewer column.</div><div><br clear="none"></div><div>Find the Gross Loser of this smaller table by identifying which row has the smallest entry, etc.</div><div><br clear="none"></div><div>The last candidate standing is the GLE winner.</div><div><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>If the challengers cannot successfully refute the claim in this manner, then the claim stands approved, and X is the winner.</div><div><br clear="none"></div><div>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><br clear="none"></div><div>Anybody have a better suggestion?</div><div><br clear="none"></div><div>Nobody?</div><div><br clear="none"></div><div><span style="font-family:sans-serif">OK, then...how do we get the proposal ball rolling?</span><br clear="none"></div><div><br clear="none"></div><div>-Forest</div><div><br clear="none"></div><div id="m_-4340217900081642727m_-8413402865815949567ydpbe4f5970yiv4345286073yqt11022"><div><br clear="none"><div><div dir="ltr">On Wed, Nov 9, 2022, 8:50 AM Forest Simmons <<a shape="rect" href="mailto:forest.simmons21@gmail.com" rel="nofollow noreferrer noreferrer" target="_blank">forest.simmons21@gmail.com</a>> wrote:<br clear="none"></div><blockquote style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div>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><br clear="none"></div><div>Elect the uncovered candidate highest in the finish order.</div><div><br clear="none"></div><div><div 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 style="font-family:sans-serif"><br clear="none"></div><div style="font-family:sans-serif">Answer: because sometimes there is no unbeaten candidate, but there is always an uncovered candidate.</div></div><div><br clear="none"></div><div>The simplest and best one-by-one elimination method is Gross Loser Elimination.</div><div><br clear="none"></div><div>No other one-at-time elimination method can improve on it, much less the uncovered version:</div><div><br clear="none"></div><div>Elect the uncovered candidate highest in the Gross Elimination finish order.</div><div><br clear="none"></div><div>Like IRV it is clone free. Unlike IRV it is precinct summable on one pass through the ballots at each precinct.</div><div><br clear="none"></div><div>Wouldn't that have been nice last night at the midterm election count?</div><div><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>GLE is already Smith efficient without the uncovered tweak ... that's just optional frosting on the cake.</div><div><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>Which team will be eliminated at this stage of GLE? </div><div><br clear="none"></div><div>Answer ... Scissors, because no other team scored as low as 35. </div><div><br clear="none"></div><div>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><br clear="none"></div><div>Now tell me, who was the IRV loser of that round?</div><div><br clear="none"></div><div>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><br clear="none"></div><div>Is this the best RCV public proposal?</div><div><br clear="none"></div><div>No other Universal Domain method this simple is anywhere near as good.</div><div><br clear="none"></div><div>How about outside the UD? Do you think STAR is a better proposal? If so why?</div><div><br clear="none"></div><div>-Forest</div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div></div><br clear="none"><div><div dir="ltr">On Wed, Nov 9, 2022, 12:05 AM Forest Simmons <<a shape="rect" href="mailto:forest.simmons21@gmail.com" rel="nofollow noreferrer noreferrer" target="_blank">forest.simmons21@gmail.com</a>> wrote:<br clear="none"></div><blockquote style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div>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><br clear="none"></div><div>Repeatedly eliminate the (remaining) candidate with fewest votes until there remains only one uncovered candidate to elect.</div><div><br clear="none"></div><div>No need to know what covering means, although you can figure it out indirectly from the definition of "uncovered:"</div><div><br clear="none"></div><div>A candidate is uncovered iff it has a beatpath of only two steps to each candidate (if any) that beats it.</div><div><br clear="none"></div><div>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><br clear="none"></div><div>When you were eliminated, you had fewer transferred votes than I.</div><div><br clear="none"></div><div>I fact, I beat every candidate pairwise that was not already eliminated (like you) on the basis of two few (transferred) votes.</div><div><br clear="none"></div><div>It is very easy to discern if some candidate X is uncovered:</div><div><br clear="none"></div><div>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><br clear="none"></div><div>X beats Z beats Y </div><div><br clear="none"></div><div>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><br clear="none"></div><div>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><br clear="none"></div><div>It's just a matter of doing regular IRV, and backing up (if necessary) until you get to an uncovered candidate.</div><div><br clear="none"></div><div>Forest</div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div><div><br clear="none"></div></div><br clear="none"><div><div dir="ltr">On Tue, Nov 8, 2022, 11:18 AM Kristofer Munsterhjelm <<a shape="rect" href="mailto:km_elmet@t-online.de" rel="nofollow noreferrer noreferrer" target="_blank">km_elmet@t-online.de</a>> wrote:<br clear="none"></div><blockquote 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 clear="none">
> Forest, what do you mean by "covered"? Is there a Wikipedia or <br clear="none">
> Electowiki article (or section of an article) that explains it? Or is <br clear="none">
> there a dictionary reference you can point to?<br clear="none">
> <br clear="none">
> Yes, you've used the words "covered" and "uncovered" many times but I <br clear="none">
> don't recall ever seeing a clear explanation of what you mean. I <br clear="none">
> presume it involves pairwise counts, but that's as far as I can guess.<br clear="none">
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The short answer is: A covers B if A pairwise beats everybody B pairwise <br clear="none">
beats and then some.<br clear="none">
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An uncovered candidate is someone who is not covered by anyone else.<br clear="none">
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This definition works when there are no pairwise ties. Things get <br clear="none">
trickier with pairwise ties, as I found out when generalizing Friendly <br clear="none">
Cover.<br clear="none">
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-km<br clear="none">
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</div></div><div id="m_-4340217900081642727m_-8413402865815949567ydpbe4f5970yqt92505">----<br clear="none">Election-Methods mailing list - see <a shape="rect" href="https://electorama.com/em" rel="nofollow noreferrer noreferrer" target="_blank">https://electorama.com/em </a>for list info<br clear="none"></div></div>
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