Approval Vote: reply to Bart Ingles

[Blake Cretney]

On Thu, 2 Mar 2000, Bart Ingles wrote:
> > "The problem of indeterminacy in approval, multiple, and truncated voting
> >  systems, Public Choice (1988), 59:101-120, by Donald G. Saari and
> >  Jill Van Newenhizen,
> 
> The titles of the latter two apparently point out Saari's objection to
> allowing voters to truncate ballots.  The version of Borda he favors
> actually penalizes truncators more than the "standard" version.  To wit:
> 
> Sincere Borda points with three candidates, for a single voter with
> preferences ABC:
> A = 2, B = 1, C = 0
> 
> Points for same candidate who truncates (standard Borda):
> A = 2, B = 0.5, C = 0.5  (or A=1.5, B = 0, C = 0)
> 
> Points for truncator in Saari's version:
> A = 1, B = 0, C = 0
> 
> (I got this directly from Prof. Saari, in response to a question)

How does Saari answer the objection that voters can just fill out their ballots randomly?  If a group of voters have preference:
A>B=C

And they fill out randomly, with about half
A>B>C
A=2 B=1 C=0
and half
A>C>B
A=2 B=0 C=1
These points average to
A=2 B=.5 C=.5

Which is why standard Borda grants these points to start with.  Why bother to allow partial rankings if you make their use impractical?

---
Blake Cretney