At 2004-01-08 20:21 +0000 Thursday, Diana Galletly wrote: >On Fri, 9 Jan 2004, Craig Carey wrote: > >> Simulated annealing is using random numbers to get around multiple >> minima. > >Why on earth does one need to "get around" multiple minima (I assume >you are talking local minima here ...) ? What is the problem with >multiple local minima? And why can't one use analytical methods to >deal with such? >
The design of preferential voting methods has functions that are partly logical, i.e. would have barriers lacking slopes allowing the typical non-linear optimizer to estimate its boundary. By 'dumb/stupid ' optimizer I meant one that performs better when there are bigger discontinuities on the 1st derivative. Researchers into the design of preferential voting methods might have to write their own optimizer since there is nothing to copy. The EM List is running in C.V.D. mode most of the time and it can't create complex programs that are suspected to be essential if man's knowledge is to be advanced. --- On the topic of the automated computation of electoral boundaries, an official could be faster (counting man-hours and not months) than an EM List numerical analyst. Anyway, who cares: the construction of advanced numerical computer programs does not seem to happen here. The list's best members seem to be flopping after 50 lines of 'for loops' or some presumbably very simple Monte Carlo random number program. -------------------------------------------------------------- I have been unsubscribed. However I scavanged through my archives for a recent unimportant message by Mr Schulze of Berlin. At 2003-12-25 00:28 +0100 Thursday, Markus Schulze wrote: >Dear Craig, > >you wrote (25 Dec 2003): >> This can be named the Alternative Vote Twin Towers example: a support ... >> http://groups.yahoo.com/group/single-transferable-vote/message/244 >> >> +-----------------------------------+ >> |Winner: � �A� � �|Winner: � �B� � �| Alternative Vote winners >> +-----------------------------------+ >> | Tot: � 513000� �| Tot: �1024001� �| >> +-----------------------------------+ >> |� �A� � � 1001� �|� �A� � 512000� �| Change = +510999 >> | * BA � � �999� �|� �BA � � 1001� �| Change = +2 >> |� �CBA� � 1000� �| * CBA� � 1000� �| >> |� �DBA� � 2000� �|� �DBA� � 2000� �| >> |� �EBA� � 4000� �|� �EBA� � 4000� �| >> |� �FBA� � 8000� �|� �FBA� � 8000� �| >> |� �GBA� �16000� �|� �GBA� �16000� �| ... >> |� �KBA� 256000� �|� �KBA� 256000� �| >> +-----------------------------------+ > >This is neither an example showing Alternative Voting violates >monotonicity nor an example showing Alternative Voting violates >participation. This is an example showing Alternative Voting >violates consistency. However, it has been demonstrated by >HP Young that only positional methods (e.g. FPP, Borda, >Approval Voting) satisfy consistency. > A pass under monotonicity removes the problem of the cascading of votes and power loss. Monotonicity itself imposes smoothness requirements by putting hard constraints on the angles by which faces can tilt and differ from FPTP's. An example very near to the above example will show a violation of monotonicity. Monotonicity can be merged in with truncation resistance or not. Persons can't simply get rid of monotonicity by stating that they have done so. Instead they must get a full list of the axioms and make sure that every axiom containing monotonicity is worded against. Maybe some of the other formulations appear to be more obviously best for a national election. Monotonicity can stop that type of example that is above so that a search does not find any. In multiwinner elections it would need to be accompanied by other multiwinner monotonicity rules that don't allow a preference to jump onto the end of the paper or off the end. That is a core mistake of Mr Schulze's "Only 5 category" pairwise comparing followers, i.e. some foul-up with bumping the last preference off the end. -- Suppose Young considered all (known and unknown) methods receiving STV ballot papers. Then the wording of Mr Schulze has 3 holes in it: [1] Mr Schulze has an unknown purpose that can can go well beyond stripping off original details and good references to accessible source allowing me to check. In fact the claim could be wrong and one that Mr Young would consider to be wrong. [2] Mr Young got it wrong. Surely that is to be suspected of university academics who don't use the word "polytope" and who have not derived fair 3 candidate methods. Economists are especially prone to having faulty and unimportant results plainly stating beliefs are certainly approximately wrong. [3] Another obvious thing is that the "Consistency" is somewhere stronger than monotonicity. So rejection of Consistency does imply anything about Monotonicity. The error perhaps gets in with the words "this is an example showing...". It could be matched up four hundreds of rules, only 40 of which can be shown to lack power. At best it was a desire to mislead or a blunder, or an instance of exercising a capacity to refer to other cellulose polymer based artefacts, and hopefully not a result of getting the implications wrong when trying to construct an argument built over some irrelevancy. Politicians-and-Polytopes: the first voting method. ---- Election-methods mailing list - see http://electorama.com/em for list info
