[EM] 03/29/02 - Rob Richie Letter and Non-Monotonicity

Adam Tarr atarr at ecn.purdue.edu
Fri Mar 29 08:20:15 PST 2002

Alex wrote:

>19% Bill > George > Ross
>18% Bill > Ross > George
>19% Ross > George > Bill
>12% Ross > Bill > George
>16% George > Bill > Ross
>16% George > Ross > Bill
>Runoff is still Bill vs. George, and George wins.  If 2% from the
>Bill>George>Ross camp list their preference as Ross>Bill>George, the runoff
>is Bill vs. Ross.  Bill wins.

Well put, Alex (in both messages).  If you want an example that sticks to the 
linear political spectrum, that can be done as well.  To wit:

44% George > Al > Ralph
15% Al > George > Ralph
15% Al > Ralph > George
26% Ralph > Al > George

Ralph loses in the first round, and Al beats George 56%-44% in the runoff.  If 
5% of the George > Al > Ralph voters switch to Ralph > George > Al, then Al 
loses in the first round and George wins the runoff 54%-46%.

This example not only shows an simple case of non-monotonicity, but does it in 
the context of the classic right/left political spectrum.  Moreover, if the 
George supporters have even approximate polling information, they know that they 
can get away with this voting trick with very little risk.  It's quite 
realistic.  There's a very large range of percentages where this exact example 

The only reason this sort of thing has not happened in Australia is because the 
third parties remain largely marginalized in their IRV elections.  Which of 
course shows the other (perhaps more important, certainly more obvious) weakness 
of IRV: it does not break the system out of a two-party duopoly.


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