# [EM] Range voting, zero-info strategy simulation

David Cary dcarysysb at yahoo.com
Wed Nov 1 22:33:06 PST 2006

```
--- raphfrk at netscape.net wrote:

>  C
>  31% of +2 -> log(7)=0.84
>  69% of +1 -> log(6)=0.78
>
>  Expected: 0.80
>
>  D
>  45% of -1 -> log(4)=0.60
>  55% of +4 -> log(9)=0.95
>
>  Expect: 0.79
>

The numbers labeled Expected: and Expect: are the expected utility of
the random event.  It is often useful to convert that back to a
certain equivalent using the inverse of the utility function.  The
incremental certain amount for C is +1.29, for D it is +1.25.  That
means that a person with a log utility function and starting position
of 5 would be indifferent between a certain offer of an additional
+1.29 and a chance to play a game that offers a 69% chance at getting
an additional +1 and a 31% chance of getting an additional +2.

In this sense, personal utility functions can vary rather
significantly, from varying shapes of risk averse (increasing and
concave), to risk neutral (an increasing straight line), to various
shapes of risk seeking (increasing convex).  The shape of a personal
utility function can vary from person to person, and is simply a
matter of personal preference.

The personal utility functions that are positive linear functions of
each other are essentially the same and are empirically
indistinquishable.  In other words, if f(x) is a utility function,
then g(x) = a * f(x) + b, for any a>0 and any b is also a utility
function that will always give the same certain equivalent amount for
a given random event.

That also means such personal utility values are useful for
describing personal indifference to uncertain outcomes, but they are
not something that can be used to aggregate utility among a group of
people.

> > A. Sincere. This voter rates the candidates sincerely even if
> this means
>  > he doesn't use the top or bottom ratings.
>  > B. Maximized sincere. This is the same as A, except that the
> best and
>  > worst candidates are moved to the 10 and 0 positions, in order
> to
>  > maximize the weight between these two candidates.

If a voter is to sincerely range vote based on their personal utility
of the outcomes, then A is not well-defined and may not be possible.

That is an example of why I sought some clarification at
http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-October/018681.html
about what exactly a sincere or honest range vote was, and what
exactly it was that Range Voting was purportedly maximizing.

-- David Cary

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