[EM] two bit ratings

[Forest Simmons]

On 28 Sep 2001, Buddha Buck wrote:

> Forest Simmons <fsimmons at pcc.edu> writes:
> 
> > I've been thinking about two bit ballot design.
> > 
> > 
> > Can anybody think of another combination of symbols with this property,
> > that they are both easily altered into a common third symbol by a stroke
> > or two of a pencil?
> 
> Well, any symbol that consists of two crossed lines would to: + -> |
> -, X -> / \, etc.
> 
> You could also do a circle and an X, with a circled X being the combination.
> 

Good suggestions.


> I haven't been following the two-bit ballot discussion too closely, so
> forgive me if this has been already discussed.  How is a two-bit ballot
> an improvement over having the voter rank the candidate on scale of 0-3? 
>  

The question is how to best represent the scale of zero to three, and how
to make the best use of it.

We want to maximize voter satisfaction. Minimize the chance for
misunderstanding. Minimize the chance of a spoiled ballot, etc.

Two bits can distinguish four states.  What should those states represent
(if not numbers)?  How should those states be encoded? 

Here's another example:

Each name on the ballot is followed by the default string  "1 -" , a one
followed by a minus sign.

The voter may alter the one, the minus sign, or both.

Any alteration of the one is considered to be a four: "1" becomes "4".

Any alteration of the minus is considered to be a plus: "-" becomes "+".

So the ballot cannot be spoiled except by crumpling it or tearing it.

After the voter has made as many alterations as she wants to and has
submitted the ballot, the codes are interpreted as follows: 

4+ > 4- > 1+ > 1-

The ballots are used to determine a round-robin, head-to-head winner by
comparing all of the candidates' scores pairwise on all of the ballots.

If no such pairwise "beats all" winner exists, then the candidate with the
greatest number of fours is the winner.

Note that if the second stage is required, the plus and minus are ignored.

There could also be an intermediate stage in which the plus and minus are
exaggerated to the extent that  "1+"  and  "4-"  are considered equal.
[Note that 1+x=4-x iff x=3/2.]

If no three-level, beats-all winner is found at this intermediate stage,
then the method falls back on the candidate with the greatest number of
fours.


Here are some other symbol transformations that might be useful in the
design of some two bit method:

r becomes n becomes m
L becomes E
L becomes 4
L becomes B
F becomes P  (so fail becomes pass)
c becomes 8
x becomes 8
3 becomes 8
u becomes a
c becomes o
c or x becomes the infinity symbol "lazy eight"
l becomes b or d
V becomes W
i becomes 4
I becomes, B,D,E,F,H,K,L,M,N,P,R,T,4,or 7.
etc.

Suppose the default string is "-c"

Any alteration of the minus is considered a plus, while any alteration of
the "c" is considered an infinity symbol.

Then in the first stage we have

+infinity > +c > -c > -infinity .

Notice that in this method the default string is not at the very bottom of
the food chain.  So the method has a Demorep style preliminary quota: all
candidates with half or more of their ratings in the negatives are
eliminated at the outset. 

The second stage sets c=0, so the middle two categories coalesce.

The last stage (when necessary) gives the win to the candidate with the
greatest number of positive ratings.

Forest