[EM] Re: Testing 1 2 3

Forest Simmons fsimmons at pcc.edu
Sun Jan 11 16:27:26 PST 2004

```On Mon, 5 Jan 2004 Dgamble997 at aol.com wrote:

> >In a realistic scenario, it's inconceivable that individual voters (even
> >hypothetical ones) would know their own preference orders, yet fail to
> >know their own utility levels for each candidate.
>
> I disagree, you have say 4 flavours of ice cream ( chocolate, mint,
> strawberry and vanilla). What is the easier task to establish a ranking or give each a
> cardinal utility rating? I finding ranking the ice creams easier than giving
> them a utility rating on a say a scale of 0 to 100.
>

Suppose that you rank the respective flavors 1, 2, 3, and 4. Then nominal
ratings would be 100%, 66.7%, 33.3%, and zero, respectively.

Evenly spaced ratings could be the default interpretation of ranked
ballots for voters that preferred rankings to ratings.

If evenly spaced ratings were published in a voters' pamphlet, the voters
could make minor adjustments to improve the accuracy.

For example, suppose that you felt that mint was a close second, and that
strawberry was somewhat closer to mint than to vanilla.  Then you could
adjust the numbers to reflect these feelings, say  100%, 90%, 50%, and
zero.

These numbers may not perfectly reflect your utilities, but they would
represent them better than mere ordinal information, i.e. ranks.

If the ballots were used for MAM, RP, SSD, IRV, etc. it wouldn't make any
instrumental difference if you used the evenly spaced ratings or the
adjusted ratings, but the satisfaction of increased expressivity is not to
be sneezed at.

More to the point of this thread (Testing 1,2,3) if we are going to
compare various methods, some of which are based on CR ballots and some of
which are based on ranked preference ballots, the simulations need some
common denominator.  Since it is easy to convert CR ballots to ranked
ballots, and problematic to go from ranked to CR, it would seem more
natural to use CR ballots as the common denominator.

Here's a sample table of evenly spaced percentages:

Two: 0,100%
Three: 0,50%,100%
Four:0,33.3%,66.7%,100%
Five:0,25%,50%,75%,100%
Six:0,20%,40%,60%,80%,100%
Seven:0,16.7%,33.3%,50%,66.7%,83.3%,100%

etc.

Forest

```