# [Election-Methods] Why monotonicity?

Juho Laatu juho.laatu at gmail.com
Tue Jan 15 12:53:26 PST 2008

```On Jan 15, 2008, at 18:22 , Steve Eppley wrote:

>> Whatever
>> you think of range voting, it is a voting system and GST, AT,
>> etc., do not
>> apply to it.
>
> (Arrow's theorem can be written to apply to Range Voting and Approval
> and all methods.  From the perspective of a math purist, to whom a
> "framework" is a non-standard way to express axioms, that's a
> better way
> to write it.  Arrow's theorem is also more powerful when rewritten to
> cover any method that chooses a winner, rather than just methods that
> return a social ordering of the alternatives.  That's how I present
> Arrow's theorem in my webpages at
> http://www.alumni.caltech.edu/~seppley, along with a proof.)

One explanation to Range and Arrow's theorem:
- social preference orderings may be cyclic
- one may arrange Range (or Approval) elections in this situation
- Range will not measure number of voters preferring X to Y (although
this can be derived from the ballots)
- strategic Range (and Approval) voters however need to decide how to
vote when there is a cycle in the social preference ordering
- let's say there is a loop A>B>C>A (preferences are e.g. 33: A>B>C,
33: B>C>A, 33: C>A>B)
- if A wins, some voters with preference B>C>A and who approved /
gave full points only to B will regret using that strategy
- also voters with preference C>A>B and who approved / gave full
points to C and A will regret if C was second

Juho

```