Thoughtful Thursday, Construction Construction Kit Two and the ACE

Protecting minority rights can be written into a Constitution. There are two cases. The easiest case, the approve case, is when the people have a plebiscite to say something is OK with them. It is a take-it-or-leave-it-proposition. The usual case is ratifying a Constitution, or voting Yes, is OK to cede sovereignty in some matter like joining the European Union, or a giving major rights to develop the country's mineral or oil resources or building a free city. The more complicated case is choosing among several alternatives. This has been studied extensively when there are n people running for a single office, e.g. President . This means that the the plebiscite has more alternatives. Allow the people to choose one of many proposed constitutions.
I discussed this briefly in the case of finalizing a peace treaty between two peoples. I explained that Israeli demos and the Palestinian Demos together would find the best peace deal for themselves without relying on their leaders to negotiate one. Simply seeing which peace deal got the most votes
total won't work. One must find one that gets the best possible approval from both
sides.

And there could have been several health care bills presented to the people.
In such a multi-candidate election, there are many techniques of converting the votes into a "Who Won?" or a ranking among candidates--approval voting, range voting, Single-Transferrable voting, Kemeny and Dodgson Scores. But these all keep all voters alike. Assume in Ethnic Group A is 55% of the population; ethnic group B is the rest. If 98% of a want to do something B really don't like such as outlawing their religion. In a simple majority or any sophisticated multi-candidated election, a could get their way. And if 60% of the A's want to do something and only 40% of B want to do it, then it will be done. But how could we design a Constitution to ensure that issues get support among both (or all) ethnic groups. Or how could we design a Constitution to encourage the legislators to prepare bills that also get support from a wide variety of individuals?

We could simply require that no bill passes unless x percentage in y percent of the ethnic groups approve the act. Thus, in our simple example above, we could require that any bill that passes earns at least 40% of the votes of each ethnic group as well as the traditional 50% of the entire population.
And the Constitution could make a broad rule of the above sort, to pass a plebiscite, in addition to getting 50% of all votes cast, it must get at least 30% of the voters in seven out of the ten designated ethnic groups.
What about a multicandidate election or a referendum with seven choices of what bill to pass. The first is simply to do whatever we were going to with the multicandidate election, but add that whatever came out of it must also pass an approve. If the winner by Dodgson score, Approval Voting or whatever method the Constitution selects, did not meet the approve criteria, where to go the next one in the ranking. See if that meets the approve criteria, otherwise, go on to the third one in the ranking. Etc.
The other option is more gentle, it adjusts or subtracts from each voting total by a deviation factor. A bill that gets the same percentage support from each ethnic group has no adjustment factor downward. A bill that gets all its support from a single ethnic group, even a majority, would have the highest adjustment factor downward.
The constitution specifies the adjustment factor.
We describe this in terms of Wally Smith's COAF system. Recall that this means that each voter gives a number for each candidate. The most general is range voting, where each candidate gives any number from one to ten, let's say. The least general, and arguably the most problematic, is the basic plurality system. Each voter gets to vote once for only one candidate. The winner is the one with the most votes.
Assume our votes came as follows in a three way election. X,Y and Z might represent candidates for the president. Or they may be one of three alternatives in a referendum.

Ethnic Group	X	Y	Z	Percentage
A	3	2	1	15
B	3	6	1	15
C	15	18	25	70
COAF SUM	2	26	27

(The percentage of the population of the ethnic group is not used in the calculation, it simply explains why the vote totals are so much higher for ethnic group C.)
The next step in calculating the ethnic group by candidate is easily done. We simply find what percentage of each ethnic group voted for each canddiate. We then average these

Ethnic Group	X	Y	Z	Percentage
a	50.00%	33.33%	16.67%
b	30.00%	60.00%	10.00%
c	25.86%	31.03%	43.10%
Average	35.29%	41.46%	23.26%

The next step is computing the deviation from the average for that candidate for each of the boxes. This gives us the the three data rows in the table below.

Ethnic Group	X	Y	Z
A	14.71%	-8.12%	-6.59%
B	-5.29%	18.54%	-13.26%
C	-9.43%	-10.42%	19.85%
Squares	216.5	66.0	43.4

Then, we sum the squares of those deviations, This a classic case of "sum of squares" or "norm two." Assume the constitution specifies an adjustment factor of 0.02. The new scores for the choices X, Y and Z. This gives us

	X	Y	z
Adjusted Score	14.3	15.6	14.7

Y won!. Thus, observe that even though Z won the popular election with 27 to 26 votes, that candidate was somewhat more skewed than y, turning the election over to Y after the adjustment factor.

nth smallest voting

There is another technique, nth smallest voting. The Constiution specifies a number nth smallest percentage is the winner. I suggested this in my first Thoughtful Thursday on the Constitution Construction Kit.
Assume, that there are seven provinces, which I call a, b, c, d, e, f and g. And assume there are three choices or candidates: X, Y and Z. And assume the Constituiton specified n = 3, or the third smallest vote,by province, determines the winning candidate. The table below states in the election of how many voted for each choice. (We allow each voter to vote for more than one alternative, like in approval voting, so the percentages don't add up to 100 per cent.)
The third smallest in each column is marked with a -.

	X	Y	z
a	38	47	43
b	12	42	42
c	13	32 -	40
d	35 -	27	34
e	60	35	37 -
f	20	28	32
g	50	50	50

Thus, the winner would be Z as its 37 for the third smallest is higher than that for other two candidates (35 and 32, respectively).

Electoral systems

The ACE Electoral District discusses many country's experiences and many statistics on how the countries choose the systems. It is a goldmine of information and analysis and suggestions for those making the decisions about constructing a Constitution. I see the fundamental division between proportional systems and geographic districts. The United States uses the latter. Each House Representative is elected from a contiguous, if not compact, district. And each voter gets to choose only one representative.
114 have districts and 35% use PR-type systems.
And twenty-two countries have some representatives being elected from districts and other representatives being elected at large or via proportional representation. A nice twist is to deal with the "wasted vote" problem. The proportional votes are distributed so as ensure that the percentage for each party matches the percentage they got fromt he whole country. E. G. Assume, there are 150 seats in parliament and 100 districts. And assume there are two parties: A and B. The top winner in each district gets elected, just like the United States. However, assume that because of the way each district votes, only 55 members of party A get elected from  the districts, and 45 of the districts B. This parallel system would then take the top 35 from the A list and 15 from the Party B-provided list. This means that the parliament would have ninety members from party A and 60 from party B--this gives the proportionality of the list system but allows each person to have a represenative for their geographical district.
And there is a really neat variation of the proportional system. The voters can rearrange the list from the parties, or just vote for a particular party.
And countries can and do use the many techniques of dealing with multiple candidate elections. Thus, if there are three people running in a district, they can simply have the one with the most votes wins, have a run off between the ones with the top two vote counts, or use one of the Hare-techniques.
And the Hare techniques can be extended to multi-member elections. Assume there are three members in a district. Those candidates getting 33% or more are chosen. Then, the bottom most candidate's second choice gets added to the total for each candidate. We then see if any of the remaining candidates got 33% votes. If not, the second choice of the second-lowest vote getter gets added to the totals. This process can continue until all the members are selected.

Minority Protection

The Ace Electoral System points out that several countries designate certain seats for specific ethnic groups including Jordan, India, Pakistan. (Also Iran reserves seats for specific groups including Zorastrians, Jews, Assyrian Christians and Armenian Christians. And of course several countries simply overrepresent certain regions in the legislature. This, of course, is done to favor ethnic groups tending to live in the area. And many nations have special arrangements for women.