(continued)
in fact, to be precise, you can look at the 4 lines of the pink table
involving R, optionally with a subset of {S,T} added (which is why 4
lines), ONLY, to see how much Nagel should subtract off the total.
Binary = 01**000000
where * means either 1 or 0.
You'll see the subtraction is of a very small amount.
(Some lines missing since zero prob.)On 9/3/10, Warren Smith <[email protected]> wrote: > On 9/3/10, Jack Nagel <[email protected]> wrote: >> Dear Warren, >> >> Thank you for sending this interesting analysis. >> >> Could you recompute the 'total paradox probabilities' without >> including 'paradoxes' or 'pathologies' R, S, and T? > > --yes... or you could, since all the necessary info to do so, is > available in the 'master table.' (I admit it is a bit of a pain.) > > Also, note T and S *ALREADY* were not included in the total paradox > probability and only {Q, R, U, V, W, X, Y, Z} were, since I did not > regard T & S as 'paradoxes' > for this purpose. So the only thing you need to remove is R. > > You can just very easily look at the blue and yellow tables > at the 2 lines for "total" and "R" and see even if every R is > removed from the total (and even if we falsely assume R and everything > else disjoint)... it doesn't change a whole lot. Actually R is > probably quite non-disjoint so > it probably changes a good deal less even than that. > >> I think that >> would be a fairer test, for these reasons: >> >> It may be fair game to criticize IRV when Paradox Y occurs (failure >> to choose the Condorcet winner), because IRV advocates point to >> greater Condorcet efficiency as one of its advantages (although it's >> rather inconsistent for you and other advocates of score and approval >> voting to do so, because you do not embrace the Condorcet criterion >> when your favorite systems do not satisfy it). Paradox Q is also OK, >> comparable to criticizing plurality for its vulnerability to spoiler >> effects. Paradoxes U, V, W, and X all appear to be variations on >> non-monotonicity, so it's fair enough to include them. >> >> But unless I've missed something, S (existence of a Condorcet cycle) >> is a not a defect of IRV, but simply a property of the underlying >> preference configuration. > > --I agree and already did agree which was why S was not in the total. > >> Indeed, IRV, like plurality, has the >> practical advantage of hiding the existence of the cycle. >> >> And how can T (IRV and plurality winners differ) be a reason for >> criticizing IRV, when plurality winners are so often faulty from any >> of several normative standpoints (including your own)? And R (the >> sniff test--IRV differs from all scoring rules), besides being a >> subset of T, again assumes as normative rules that are much debated. > > --again I agree and already did agree and was why T was not in the total. > T is of interest for defining two different subpopulations of elections > though. > > You appear not to have said in your email why you do not like R(?), > but anyhow as I said if you remove R it won't change things a whole > lot since R is fairly rare. > > -- > Warren D. Smith > http://RangeVoting.org <-- add your endorsement (by clicking > "endorse" as 1st step) > and > math.temple.edu/~wds/homepage/works.html > -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info
