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Scirocco (old). On ten by ten board with over thirty different pieces. (10x10, Cells: 100) [All Comments] [Add Comment or Rating]

🕸Fergus Duniho wrote on Thu, Dec 8, 2005 11:54 PM UTC:

Let me offer some parallels here. According to Gödel's Incompleteness
Theorem, any sufficiently comprehensive system of logic will be
incomplete. The ideal logical system would be both comprehensive and
complete, but Gödel has shown that this can't be. According to Arrow's
Impossibility Theorem, 'There is no consistent method by which a
democratic society can make a choice (when voting) that is always fair
when that choice must be made from among 3 or more alternatives.' As
Steve Eppley puts it, it shows 'that no voting method can, in every
voting scenario, satisfy a certain set of desirable criteria:
non-dictatorship, unanimity, rationality, and 
independence from irrelevant alternatives (IIA).  Thus no voting method is
ideal.' The basic idea behind both of these is that some of the ideal
characteristics of a system, whether a logical system or a ballot counting
system, are incompatible with each other. It may also hold for Chess
variants that all the ideal characteristics of a Chess variant cannot
compatibly coexist in the same game. If that is so, then the ideal Chess
variant is a pipedream.