<html><head></head><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12px"><div id="yui_3_16_0_1_1480194238064_14985"><font size="3" id="yui_3_16_0_1_1480194238064_15313">Hi Kristofer,</font></div><div id="yui_3_16_0_1_1480194238064_14986"><font size="3"><br id="yui_3_16_0_1_1480194238064_14987"></font></div><div id="yui_3_16_0_1_1480194238064_14988"><font size="3">De : Kristofer Munsterhjelm <km_elmet@t-online.de></font></div><div id="yui_3_16_0_1_1480194238064_14989"><font size="3">À : Kevin Venzke <stepjak@yahoo.fr>; EM list <election-methods@electorama.com> </font></div><div id="yui_3_16_0_1_1480194238064_14990"><font size="3">Envoyé le : Samedi 26 novembre 2016 7h25</font></div><div id="yui_3_16_0_1_1480194238064_14991"><font size="3">Objet : Re: [EM] Method space of 3-bloc, strictly-ranked scenarios</font></div><div id="yui_3_16_0_1_1480194238064_14992"><font size="3"><br id="yui_3_16_0_1_1480194238064_14993"></font></div><div id="yui_3_16_0_1_1480194238064_14994"><font size="3">>> ABABAACC: The MinMax group. This includes most MinMax methods (including</font></div><div id="yui_3_16_0_1_1480194238064_14995"><font size="3">>> also Schulze, MAM, etc.), DMC, Approval-Elimination Runoff, MAMPO, some</font></div><div id="yui_3_16_0_1_1480194238064_14996"><font size="3">>> scenarios of Kristofer's "linear" Condorcet method, a couple of obscure</font></div><div id="yui_3_16_0_1_1480194238064_14997"><font size="3">>> Woodall methods (MinGS and 3MaxGS), Condorcet//FPP, and probably a lot</font></div><div id="yui_3_16_0_1_1480194238064_14998"><font size="3">>> of other methods.</font></div><div id="yui_3_16_0_1_1480194238064_14999"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15000"><font size="3">>> ABABABCC: Condorcet//IRV group, including Raynaud, Condorcet//KH, and</font></div><div id="yui_3_16_0_1_1480194238064_15001"><font size="3">>> most scenarios of Kristofer's "linear" method. Off the top of my head it</font></div><div id="yui_3_16_0_1_1480194238064_15002"><font size="3">>> should also include the "Woodall" and "Benham" methods.</font></div><div id="yui_3_16_0_1_1480194238064_15003"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15004"><font size="3">>So the linear methods are somewhat more Minimax-y C//IRVs. That sort of</font></div><div id="yui_3_16_0_1_1480194238064_15005"><font size="3">>makes sense, in particular when even Condorcet/FPP is considered</font></div><div id="yui_3_16_0_1_1480194238064_15006"><font size="3">>Minmaxy. Moving closer to minmax makes the methods more monotone, but</font></div><div id="yui_3_16_0_1_1480194238064_15007"><font size="3">>they're still similar to C//IRV in being strategy resistant Condorcet</font></div><div id="yui_3_16_0_1_1480194238064_15008"><font size="3">>methods.</font></div><div id="yui_3_16_0_1_1480194238064_15009"><font size="3"><br id="yui_3_16_0_1_1480194238064_15010"></font></div><div id="yui_3_16_0_1_1480194238064_15011"><font size="3">Sounds right although, within this framework, I can't even show that IRV </font></div><div id="yui_3_16_0_1_1480194238064_15012"><font size="3">is not monotone. I wonder if there could be a different cause of undesirable</font></div><div id="yui_3_16_0_1_1480194238064_15013"><font size="3">behavior. Of the properties I have (and which make sense in the 8-scenario </font></div><div id="yui_3_16_0_1_1480194238064_15014"><font size="3">case), C//IRV lacks two properties compared to the MinMax group: it violates</font></div><div id="yui_3_16_0_1_1480194238064_15015"><font size="3">a sort of mono-remove-bottom, and a property I can't quite generalize into </font></div><div id="yui_3_16_0_1_1480194238064_15016"><font size="3">words which says that the last choice of the largest faction shouldn't be</font></div><div id="yui_3_16_0_1_1480194238064_15017"><font size="3">elected.</font></div><div id="yui_3_16_0_1_1480194238064_15018"><font size="3"><br id="yui_3_16_0_1_1480194238064_15019"></font></div><div id="yui_3_16_0_1_1480194238064_15020"><font size="3">(Incidentally the MinMax and C//IRV groups are the only Condorcet ones </font></div><div id="yui_3_16_0_1_1480194238064_15021"><font size="3">that satisfy a sort of participation property, in that a faction's last</font></div><div id="yui_3_16_0_1_1480194238064_15022"><font size="3">choice should not be elected if the withdrawal of that faction would elect</font></div><div id="yui_3_16_0_1_1480194238064_15023"><font size="3">their compromise choice.)</font></div><div id="yui_3_16_0_1_1480194238064_15024"><font size="3"><br id="yui_3_16_0_1_1480194238064_15025"></font></div><div id="yui_3_16_0_1_1480194238064_15026"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15027"><font size="3">>> ABCBABCC: BPW (Eivind Stensholt's "Beats Plurality Winner" Condorcet</font></div><div id="yui_3_16_0_1_1480194238064_15028"><font size="3">>> method).</font></div><div id="yui_3_16_0_1_1480194238064_15029"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15030"><font size="3">>Stensholt also has another method (which he has called SV):</font></div><div id="yui_3_16_0_1_1480194238064_15031"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15032"><font size="3">>Let F(X) be the fraction of voters who gave X a first preference vote</font></div><div id="yui_3_16_0_1_1480194238064_15033"><font size="3">>(e.g. F(A) = 0.5 is half the voters put A first).</font></div><div id="yui_3_16_0_1_1480194238064_15034"><font size="3">>Let a = 1/2 - F(A), b = 1/2 - F(B), g = 1/2 - F(C).</font></div><div id="yui_3_16_0_1_1480194238064_15035"><font size="3">>If there's no cycle, the CW wins, otherwise WLOG suppose it's an ABCA</font></div><div id="yui_3_16_0_1_1480194238064_15036"><font size="3">>cycle. Then A's penalty is b/g, B's is g/a, and C's is a/b. Minimum</font></div><div id="yui_3_16_0_1_1480194238064_15037"><font size="3">>penalty wins.</font></div><div id="yui_3_16_0_1_1480194238064_15038"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15039"><font size="3">>I guess this would produce the same results as BPW, but you could check.</font></div><div id="yui_3_16_0_1_1480194238064_15040"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15041"><font size="3">>In my post about linear methods, I also mentioned this nonlinear method:</font></div><div id="yui_3_16_0_1_1480194238064_15042"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15043"><font size="3">>Again WLOG let the cycle be ABCA. Then the scores are</font></div><div id="yui_3_16_0_1_1480194238064_15044"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15045"><font size="3">>A's score: A>B * min(C>A, A>B)/fpC</font></div><div id="yui_3_16_0_1_1480194238064_15046"><font size="3">>B's score: B>C * min(A>B, B>C)/fpA</font></div><div id="yui_3_16_0_1_1480194238064_15047"><font size="3">>C's score: C>A * min(B>C, C>A)/fpB</font></div><div id="yui_3_16_0_1_1480194238064_15048"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15049"><font size="3">>and greatest score wins. fpX is the number of first preferences for X.</font></div><div id="yui_3_16_0_1_1480194238064_15050"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15051"><font size="3">>I kind of suspect the min() part is related to beatpaths. Isn't min(C>A,</font></div><div id="yui_3_16_0_1_1480194238064_15052"><font size="3">>A>B) the strength of the beatpath from C to B, i.e. from who beat A to</font></div><div id="yui_3_16_0_1_1480194238064_15053"><font size="3">>who A beats? Of course, the optimizer has no idea what concept it's finding.</font></div><div id="yui_3_16_0_1_1480194238064_15054"><font size="3"><br id="yui_3_16_0_1_1480194238064_15055"></font></div><div id="yui_3_16_0_1_1480194238064_15056"><font size="3">Ok. I didn't know about Stensholt's other method, and I should check it out. </font></div><div id="yui_3_16_0_1_1480194238064_15057"><font size="3">And I did bring up our old emails to review the nonlinear method. The trouble</font></div><div id="yui_3_16_0_1_1480194238064_15058"><font size="3">is that methods that are sensitive to the "absolute" size differences between</font></div><div id="yui_3_16_0_1_1480194238064_15059"><font size="3">the factions, tend to produce more than one DNA code. That's what was going</font></div><div id="yui_3_16_0_1_1480194238064_15060"><font size="3">on when you see that I put the linear method under two groups: It has two </font></div><div id="yui_3_16_0_1_1480194238064_15061"><font size="3">codes. Most methods (even with 343 digits) only have one. But e.g. </font></div><div id="yui_3_16_0_1_1480194238064_15062"><font size="3">MinMax(margins) has seven, and FPP(ER-Fractional) has twelve...</font></div><div id="yui_3_16_0_1_1480194238064_15063"><font size="3"><br id="yui_3_16_0_1_1480194238064_15064"></font></div><div id="yui_3_16_0_1_1480194238064_15065"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15066"><font size="3">>You could also try BTR-IRV, which is IRV-like but sometimes not. It</font></div><div id="yui_3_16_0_1_1480194238064_15067"><font size="3">>consists of, in every round, beat whoever pairwise loses to the other of</font></div><div id="yui_3_16_0_1_1480194238064_15068"><font size="3">>the last two candidates sorted by Plurality count. It would be more like</font></div><div id="yui_3_16_0_1_1480194238064_15069"><font size="3">>the "always eliminate the second to last finisher" than plain IRV is.</font></div><div id="yui_3_16_0_1_1480194238064_15070"><font size="3"><br id="yui_3_16_0_1_1480194238064_15071"></font></div><div id="yui_3_16_0_1_1480194238064_15072"><font size="3">I forgot about BTR-IRV. I'll definitely add that one (it's unusual, and easy</font></div><div id="yui_3_16_0_1_1480194238064_15073"><font size="3">to code). At a glance I believe that one falls under the MinMax group, though.</font></div><div id="yui_3_16_0_1_1480194238064_15074"><font size="3"><br id="yui_3_16_0_1_1480194238064_15075"></font></div><div id="yui_3_16_0_1_1480194238064_15076"><font size="3">I should say once we add in other ballot types the plot changes quite a bit.</font></div><div id="yui_3_16_0_1_1480194238064_15077"><font size="3">E.g. on the plot I just posted, DAC/DSC are a single point. But when we add in</font></div><div id="yui_3_16_0_1_1480194238064_15078"><font size="3">bullet votes they tend to be on opposite ends of one axis.</font></div><div id="yui_3_16_0_1_1480194238064_15079"><font size="3"><br id="yui_3_16_0_1_1480194238064_15080"></font></div><div id="yui_3_16_0_1_1480194238064_15081"><font size="3">> </font></div><div id="yui_3_16_0_1_1480194238064_15082"><font size="3">>> Here is an attempt at plotting the Hamming distances of these codes, so</font></div><div id="yui_3_16_0_1_1480194238064_15083"><font size="3">>> that more similar methods are plotted closer together:</font></div><div id="yui_3_16_0_1_1480194238064_15084"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15085"><font size="3">>[snip]</font></div><div id="yui_3_16_0_1_1480194238064_15086"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15087"><font size="3">>I was thinking about something similar the other day. You could do this:</font></div><div id="yui_3_16_0_1_1480194238064_15088"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15089"><font size="3">>Let each method's feature vector be something like:</font></div><div id="yui_3_16_0_1_1480194238064_15090"><font size="3">>--first letter--, --second--, --third-- ...</font></div><div id="yui_3_16_0_1_1480194238064_15091"><font size="3">>[is it A?, is B? is C? A?, B?, C? A?, B?, C? ]</font></div><div id="yui_3_16_0_1_1480194238064_15092"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15093"><font size="3">>1 if true, 0 if false. So, for instance, a method that starts in ABC</font></div><div id="yui_3_16_0_1_1480194238064_15094"><font size="3">>would have a feature vector starting in</font></div><div id="yui_3_16_0_1_1480194238064_15095"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15096"><font size="3">>[1, 0, 0, 0, 1, 0, 0, 0, 1, ....]</font></div><div id="yui_3_16_0_1_1480194238064_15097"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15098"><font size="3">>If you take the Euclidean distance between two different methods'</font></div><div id="yui_3_16_0_1_1480194238064_15099"><font size="3">>feature vectors, you should get twice the Hamming distance. (If method X</font></div><div id="yui_3_16_0_1_1480194238064_15100"><font size="3">>and Y agree on the first letter, that contributes 0 to the distance, but</font></div><div id="yui_3_16_0_1_1480194238064_15101"><font size="3">>if they disagree, that contributes 1 to the distance)</font></div><div id="yui_3_16_0_1_1480194238064_15102"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15103"><font size="3">>Now make a matrix of all the methods' feature vectors, run SVD on it,</font></div><div id="yui_3_16_0_1_1480194238064_15104"><font size="3">>and pick the two first singular vectors (corresponding to the greatest</font></div><div id="yui_3_16_0_1_1480194238064_15105"><font size="3">>singular values). Multiply them by their respective singular values, let</font></div><div id="yui_3_16_0_1_1480194238064_15106"><font size="3">>the resulting vectors give the x and y coordinates, and plot.</font></div><div id="yui_3_16_0_1_1480194238064_15107"><font size="3"><br id="yui_3_16_0_1_1480194238064_15108"></font></div><div id="yui_3_16_0_1_1480194238064_15109"><font size="3">Uh oh. I had to google SVD.</font></div><div id="yui_3_16_0_1_1480194238064_15110"><font size="3"><br id="yui_3_16_0_1_1480194238064_15111"></font></div><div id="yui_3_16_0_1_1480194238064_15112"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15113"><font size="3">>This can in theory be done on any dimension feature vector, so you could</font></div><div id="yui_3_16_0_1_1480194238064_15114"><font size="3">>collapse the 343-digit codes to two dimensions that way as well, or even</font></div><div id="yui_3_16_0_1_1480194238064_15115"><font size="3">>consider each particular election that way (e.g. if you test on 100k</font></div><div id="yui_3_16_0_1_1480194238064_15116"><font size="3">>elections, the vector would be 300k long). You could model methods that</font></div><div id="yui_3_16_0_1_1480194238064_15117"><font size="3">>fit partly in the camp as well, if you'd like, e.g.</font></div><div id="yui_3_16_0_1_1480194238064_15118"><font size="3"><br id="yui_3_16_0_1_1480194238064_15119"></font></div><div id="yui_3_16_0_1_1480194238064_15120"><font size="3">I can say part of the motivation for the 343 is to not have to do </font></div><div id="yui_3_16_0_1_1480194238064_15121"><font size="3">simulations, and be able to exhaustively investigate a method. (Or at</font></div><div id="yui_3_16_0_1_1480194238064_15122"><font size="3">least its representation within the framework...)</font></div><div id="yui_3_16_0_1_1480194238064_15123"><font size="3"><br id="yui_3_16_0_1_1480194238064_15124"></font></div><div id="yui_3_16_0_1_1480194238064_15125"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15126"><font size="3">>[0.5, 0.5, 0, ...]</font></div><div id="yui_3_16_0_1_1480194238064_15127"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15128"><font size="3">>is a method that, in the first scenario set, elects A half the time, B</font></div><div id="yui_3_16_0_1_1480194238064_15129"><font size="3">>the other half, and never elects C.</font></div><div id="yui_3_16_0_1_1480194238064_15130"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15131"><font size="3">>Another possibility as far as plotting goes is to use a synthetic</font></div><div id="yui_3_16_0_1_1480194238064_15132"><font size="3">>coordinate algorithm to determine points on a plane that give distances</font></div><div id="yui_3_16_0_1_1480194238064_15133"><font size="3">>most like the distances you have already calculated. Such distances</font></div><div id="yui_3_16_0_1_1480194238064_15134"><font size="3">>could be sums of Kendall-tau distances between the different methods'</font></div><div id="yui_3_16_0_1_1480194238064_15135"><font size="3" id="yui_3_16_0_1_1480194238064_15311">>social orderings. I did that once, and you commented that the plot</font></div><div id="yui_3_16_0_1_1480194238064_15136"><font size="3" id="yui_3_16_0_1_1480194238064_15310">>didn't seem to make much sense beyond the rough scale: all Condorcet</font></div><div id="yui_3_16_0_1_1480194238064_15137"><font size="3" id="yui_3_16_0_1_1480194238064_15309">>methods gathered together in the middle, and then Plurality was off to</font></div><div id="yui_3_16_0_1_1480194238064_15138"><font size="3">>one side and Random Ballot off to another, I think.</font></div><div id="yui_3_16_0_1_1480194238064_15139"><font size="3"><br id="yui_3_16_0_1_1480194238064_15140"></font></div><div id="yui_3_16_0_1_1480194238064_15141"><font size="3">Hmm, I think I remember that.</font></div><div id="yui_3_16_0_1_1480194238064_15142"><font size="3"><br id="yui_3_16_0_1_1480194238064_15143"></font></div><div id="yui_3_16_0_1_1480194238064_15144"><font size="3" id="yui_3_16_0_1_1480194238064_15325">The way the plotting works now is that it finds the Hamming distances</font></div><div id="yui_3_16_0_1_1480194238064_15145"><font size="3" id="yui_3_16_0_1_1480194238064_15308">(using however many digits of DNA) and then plots methods one-by-one in</font></div><div id="yui_3_16_0_1_1480194238064_15146"><font size="3" id="yui_3_16_0_1_1480194238064_15307">2D space, trying to reduce the sum of squares of difference between the</font></div><div id="yui_3_16_0_1_1480194238064_15147"><font size="3" id="yui_3_16_0_1_1480194238064_15324">Hamming distance and the apparent Euclidean distance. The whole thing is</font></div><div id="yui_3_16_0_1_1480194238064_15148"><font size="3" id="yui_3_16_0_1_1480194238064_15323">done a number of times and with the methods in randomized order, keeping</font></div><div id="yui_3_16_0_1_1480194238064_15149"><font size="3">the best result.</font></div><div id="yui_3_16_0_1_1480194238064_15150"><font size="3"><br id="yui_3_16_0_1_1480194238064_15151"></font></div><div id="yui_3_16_0_1_1480194238064_15152"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15153"><font size="3">>If you have an n*n method-method distance matrix (where d[a][b] gives</font></div><div id="yui_3_16_0_1_1480194238064_15154"><font size="3">>some distance between methods, e.g. by the Kendall tau distance), you</font></div><div id="yui_3_16_0_1_1480194238064_15155"><font size="3">>could also use a hierarchical clustering algorithm to get something</font></div><div id="yui_3_16_0_1_1480194238064_15156"><font size="3">>analogous to a cladogram or phylogenetic tree - a dendrogram. I think I</font></div><div id="yui_3_16_0_1_1480194238064_15157"><font size="3">>did that once, too, and though I didn't post my results, it seemed to</font></div><div id="yui_3_16_0_1_1480194238064_15158"><font size="3">>make more sense than the synthetic coordinate diagram. You might end up</font></div><div id="yui_3_16_0_1_1480194238064_15159"><font size="3">>with something like...</font></div><div id="yui_3_16_0_1_1480194238064_15160"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15161"><font size="3">> +---Carey</font></div><div id="yui_3_16_0_1_1480194238064_15162"><font size="3">> +--IRV--+</font></div><div id="yui_3_16_0_1_1480194238064_15163"><font size="3">> | +----Plurality</font></div><div id="yui_3_16_0_1_1480194238064_15164"><font size="3">> |</font></div><div id="yui_3_16_0_1_1480194238064_15165"><font size="3">>all----+</font></div><div id="yui_3_16_0_1_1480194238064_15166"><font size="3">> |</font></div><div id="yui_3_16_0_1_1480194238064_15167"><font size="3">> | +---Borda</font></div><div id="yui_3_16_0_1_1480194238064_15168"><font size="3">> +--Sinkhorn--+</font></div><div id="yui_3_16_0_1_1480194238064_15169"><font size="3">> +---Schulze</font></div><div id="yui_3_16_0_1_1480194238064_15170"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15171"><font size="3"><br id="yui_3_16_0_1_1480194238064_15172"></font></div><div id="yui_3_16_0_1_1480194238064_15173"><font size="3">That's a neat idea. I'll need to read up on how this algorithm can work</font></div><div id="yui_3_16_0_1_1480194238064_15174"><font size="3">though. Sometimes a strange method gets plotted out in space and I don't</font></div><div id="yui_3_16_0_1_1480194238064_15175"><font size="3">know how arbitrary its placement is wrt the methods it appears to be closest</font></div><div id="yui_3_16_0_1_1480194238064_15176"><font size="3">to. A tree would probably be helpful there.</font></div><div id="yui_3_16_0_1_1480194238064_15177"><font size="3"><br id="yui_3_16_0_1_1480194238064_15178"></font></div><div id="yui_3_16_0_1_1480194238064_15179"><font size="3">></font></div><div id="yui_3_16_0_1_1480194238064_15180"><font size="3">>> In all of those 6561, only nine of them are Condorcet methods. I can</font></div><div id="yui_3_16_0_1_1480194238064_15181"><font size="3">>> describe all of them:</font></div><div id="yui_3_16_0_1_1480194238064_15182"><font size="3">>> </font></div><div id="yui_3_16_0_1_1480194238064_15183"><font size="3">>> ABABAACC: MinMax</font></div><div id="yui_3_16_0_1_1480194238064_15184"><font size="3">>> ABABABCC: C//IRV</font></div><div id="yui_3_16_0_1_1480194238064_15185"><font size="3">>> ABABACCC: C//QR</font></div><div id="yui_3_16_0_1_1480194238064_15186"><font size="3">>> ABBBAACC: Bucklin</font></div><div id="yui_3_16_0_1_1480194238064_15187"><font size="3">>> ABBBABCC: (???) always elect B in a cycle</font></div><div id="yui_3_16_0_1_1480194238064_15188"><font size="3" id="yui_3_16_0_1_1480194238064_15360">>Wouldn't that one fail neutrality? Suppose the cycle is ABCA. You could</font></div><div id="yui_3_16_0_1_1480194238064_15189"><font size="3">>always relabel the candidates by following the cycle.</font></div><div id="yui_3_16_0_1_1480194238064_15190"><font size="3"><br id="yui_3_16_0_1_1480194238064_15191"></font></div><div id="yui_3_16_0_1_1480194238064_15192"><font size="3" id="yui_3_16_0_1_1480194238064_15361">Not neutrality, because the candidates are labeled by faction size. The </font></div><div id="yui_3_16_0_1_1480194238064_15193"><font size="3" id="yui_3_16_0_1_1480194238064_15362">problem is that the A faction may wish they had received fewer votes so</font></div><div id="yui_3_16_0_1_1480194238064_15194"><font size="3">that their candidate could be the one labeled "B."</font></div><div id="yui_3_16_0_1_1480194238064_15195"><font size="3"><br id="yui_3_16_0_1_1480194238064_15196"></font></div><div id="yui_3_16_0_1_1480194238064_15197"><font size="3">I actually made an unexpected amount of progress today evaluating the</font></div><div id="yui_3_16_0_1_1480194238064_15198"><font size="3" id="yui_3_16_0_1_1480194238064_15363">properties of all 6561 methods. I think probably only a handful more are</font></div><div id="yui_3_16_0_1_1480194238064_15199"><font size="3">worth mentioning...</font></div><div id="yui_3_16_0_1_1480194238064_15200"><font size="3"><br id="yui_3_16_0_1_1480194238064_15201"></font></div><div id="yui_3_16_0_1_1480194238064_15202"><font size="3">Kevin</font></div><div dir="ltr" id="yui_3_16_0_1_1480194238064_15203"><br id="yui_3_16_0_1_1480194238064_15204"></div></div></body></html>