# Proposed MMP ballot initiative in Colorado

Olli Salmi olli.salmi at utu.fi
Thu Apr 23 09:21:28 PDT 1998

```>You wrote:
>>Not bad. The voters have some say over the party list so I think this is
>>better than the New Zealand system.
>
>Don writes: I failed to see that the voters have some say over the party
>list. What do you see in the Colorado initiative that gives the voters some
>say?

If a candidate that's not high on the party list is very popular, he/she
can be elected. Of course the voters can't influence the list before the
election (unless they are party members).

>You wrote:
>>Why do you use the largest remainder method? It produces erratic results.
>>Why not use Sainte-Lague/Webster?
>
>Don writes: The largest remainder is not the best method but it does have
>some logic to its use - the largest remainder get the remainder seats.
>
>     You have raised the suggestion of Sainte-Lague before and you have
>explained how it works very well and I understand the mechanics of it - but
>I do not see the logic of why it should be used. In other words, why is
>Sainte-Lague a valid method to use to resolve the remainders?
>
>     It appears to me that these divisor methods are merely simple
>mathematical games that we can play for amusement, but without any reason
>why they should be used in an election.
>
>     Could you - would you explain why divisors should be allowed to
>resolve the remainders?

If the number of seats in the legislature or committee is increased, a
party may lose seats with the same number of votes with the largest
remainder method. That's what I mean by erratic. Still, the system is used
in many countries and it is easy to understand.

I just found something I had written for myself several years ago, on my
Commodore 64 apparently. Let us suppose there are four parties:

A	550
B	470
C	250
D	170

19 seats would be allocated between the parties like this (apparently I've
used TotalNumberOfVotes/NumberOfSeats as the quota):

Party	Quotient	Seats
A	7.26		7
B	6.20		6
C	3.30		4
D	2.24		2

20 seats would be allocated between the parties like this:

Party	Quotient	Seats
A	7.64		8
B	6.53		7
C	3.47		3
D	2.36		2

Party C would lose a seat, even if the total is increased. Erratic. Unfair.

If you think the divisor method is a mathematical game, it's possible that
you haven't understood them properly. The idea behind both D'Hondt and
Sainte-Lague is (as I may have explained before) that you try to find such
a quota that all seats are filled. You divide the total number of votes for
the party by the quota, and the quotient, truncated in D'Hondt, rounded in
Sainte-Lague, is the number of seats for the party. There is no formula to
calculate the quota, so it is arrived at by dividing consecutively with a
series of divisors.

D'Hondt favours big parties. If party A has 10900 votes and party B 1900
votes with a quota of 1000, party A would get 10 seats and party B one
seat. The average number of votes per seat is 1090 for party A and 1900 for
party B. Small parties have a disadvantage because the quotient is
truncated, every party wastes votes and the bigger the number of seats for
the party the smaller the waste *per seat* (the total number of wasted
votes never exceeds the quota). This is how I understand it, but it might
be mathematically incorrect. I refer you to the book Fair Representation by
Michael L. Balinski & H. Peyton Young, New Haven 1982 for the mathematics.

In Saint-Lague both small and big parties gain and lose equally from the
rounding.

I don't know the mathematics from the point of view of STV. You could try
to generate random voting results assuming that all voters vote a straight
ticket, keeping the total number of votes and seats constant. Then you
would calculate what the average number of votes needed to elect a
candidate is. If it's the same for a party with ten seats and a party with
one seat, the system is rather equitable.

Sorry about the length of this message (it's long perhaps becauce I was
supposed to be doing some hoovering and tidying up). I also apologize for
quoting the whole Colorado proposal in my previous message. I intended to
erase it.

Regards,

Olli Salmi

```