> From: Jonathan Lundell <[email protected]> > To: "Terry Bouricius" <[email protected]> > Cc: [email protected], [email protected] > Subject: Re: [EM] I need an example of Condorcet method being > subjected > Message-ID: <[email protected]> > Content-Type: text/plain; charset=us-ascii > > On Jan 22, 2010, at 10:30 AM, Terry Bouricius wrote: > >> Jonathan, >> >> Yes and no...You are correct that Arrow never uses the term >> "monotonicity," but the concept is embodied in his second condition, >> called "positive association." > > Yes--I'm talking about terminology merely (that, and that "monotonicity" > itself needs definition in a particular context). >
Jonathan, Monotonicity is a mathematical concept that is fairly simple to describe. There is non-decreasing monotonicity, strictly increasing monotonicity, non-increasing monotonicity, etc. Arrow describes the concept re. elections fairly well in one of his fairness conditions. IRV/STV are the only alternative voting methods I am aware of that fail this monotonicity condition that Arrow's fairness condition requires but I have not studied all alternative methods so there must be others that fail Arrow's monotonicity criteria. Plurality elections do *not* fail this criteria which is why IRV/STV fail more of Arrow's fairness criteria than plurality does. The simplest way to state it in English is that the act of voting in any one election should be monotonically increasing by giving the voter the right to know that voting for a candidate always increases that candidate's chances of winning holding all other things constant (given the votes of other voters). In other words, mathematically, increasing the input or x value, always increases the output or y value in a monotonically increasing function. IRV/STV are the only methods I know that fail the monotonicity test and thus deprive the voters the right to know what effect, positive or negative, their ballot will have on the candidates the voter votes for, but I'm sure there must be others. And please do not repeat the BS about plurality failing monotonicity because you incorrectly think of general and primary elections as being one election, because in each plurality election the voter retains the right to help the candidates of their choosing to win each election, so a voter can knowingly strategize effectively if the voter chooses to, unlike with IRV/STV where, for instance in the recent Aspen election if 75 fewer voters had voted for one of the city council members, he would have won instead of losing. What an insane voting method! -- Kathy Dopp Town of Colonie, NY 12304 phone 518-952-4030 cell 518-505-0220 http://utahcountvotes.org http://electionmathematics.org http://kathydopp.com/serendipity/ Realities Mar Instant Runoff Voting http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf Voters Have Reason to Worry http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf Checking election outcome accuracy --- Post-election audit sampling http://electionmathematics.org/em-audits/US/PEAuditSamplingMethods.pdf ---- Election-Methods mailing list - see http://electorama.com/em for list info
