Miscellaneous

Referendum News

This November, San Francisco will have
a referendum
might be unconstitutional as Jews and Moslems practice circumcision for
religious reasons. It also would be ineffective, as people could easily
have the procedure down outside San Francisco limits. It is sad that
referendums, a wonderful tool, are used for such silliness when Californians
have very pressing problems.

On the subject of silliness in California Referendums, Amazon is using the
referendum process so it does not have to collect sales tax, even though
it "has a physical presence in the state."

Unfortunately, it will probably end in court--apparently in.
California, budget related
laws and "laws that take effect immediately" can't be referendum-vetoed

And one borough is dealing with anti-budget referendum by a clause in its. And there is a move to discourage voting.
bylaws that says fifteen percent of the voters must vote in a referendum--otherwise the referendum is null and void

And Maryland is going to have a referendum on whether undocumented immigrants.
will be eligible for in-state tuition in the Universities

New Zealand will vote on which parliamentary voting system it will use:

1. 
   Currently they use mixed-member proportional with 70 chosen from districts
   and fifty thorugh party lists
2. 
   single transferable vote with some districts electing more than one member
   of parliament
3. 
   a conventinal system like what the United States does, where each district
   elects one represenative.
4. 
   A variation of this with single transferable
5. 
   and a variation on MMP, but where they don't try to adjust the party list members
   to ensure tghat the percentage of each party in parliament matches the total
   voting.

I discussed many of these voting options in my last Thoughtful Thursday posting.

Apparently, the voters will choose on two questions and then there will (I would be in favor of using approval.)
be another referendum in 2014.
voting here between the systems

Anti-nuclear referndum are popular world wide. Poland is planning one on shelving
building their own that were planning.

Italy voted against nuclear energy. Voters also rejected immunity for government officials, so they could
concentrate on their official duties. This is a referendum on Berlusconi who
would have to attend four separate trials.

Health Care

The new health care law allows businesses to pay two thousand dollars
instead of insuring its workers. At that point the workers move into
subsidized "exchanges." There is debate about how many businesses will But Freakonomics reports that when a day care center
take that option. And small businesses less than fifty employees pay nothing
if they choose not to pay their employee's health insurance.
moved from no fine for coming late to pick up your child to a three-dollar
fine, more parents were tardy to collect their kids. Sometimes, people
will take a minor penalty when given that option. With no penalty, moral
pressure will get them to do the "right thing" whether that be picking
up their kid on time or health insuring their workers.
In any event, my suggestion is to apply a sales tax based upon.
the business's provision of health insurance, among other factors.

Businesses would compete to be good businesses, and that includes

taking care of their workers.

elatedly, the June 28th issue of the New York Times (Andrew Pollack, page one)
reported on drugs that
extend the lives of a small percentage of prostate cancer sufferers, those
who are unfortunate enough to have the cancer goe beyond the prostrate and
for which hormone therapy has not worked. This is the question of whether
a few billion dollars is worth what appears to be a modest extension of survival.

And the Wall Street Journal just reported on several drugs that
are truly innovative as opposed to a me-too product. They include a new
drug for advanced melanoma, the first drug for lupus in over fifty years,
and improvements in hepatitis C care.

Of course, I propose that we have a fixed amount of money for drug innovations.

The drug companies would innovate to achieve the best improvements and try
to find drugs that work where no drug has worked before, as contrasted with
me-oo drugs.

Then, the money would be given to the teams and companies achieving the best
outcome, compared to current care.

Admittedly, the insurance companies are achieving this outcome already, by simply
demanding that their patients use generic drugs when such are available and
the new pharmaceutical, under patent protection, dosn't do much better.

Good Statistics, in 2006, pharmaceutical firms spent 45.8 billion on research,
17 percent of their revenue.
("Drug Makers Refill Prched Pipelines", by Jonathan D. Rockoff and Ron Winslow,
July 11 2011 BVol CCLVIII No 8, Wall Street Journal, pages A1, A12)

Another pork barrel project

Representative John L. Mica, who happens to be chairman of the House
Transportation and Infrastructure Committee, has pushed through a 61 mile
ommuter ail prject. The federal government ranks it as one of the least
cost-effective, only projected to serve 2100 people per day. Althougn in

Central Florida, it does not serve the Orlando Airport or Disney world attraction. The Federal government will pay CSX $432 million
for the use of its tracks. CSX and other contractors have contributed to
r. Mica's campaign.

All government projects should go before a sortition jury for approval.
New York TimesJune 28th, pages A1 and A3, "A Congressman's Pet Project;
a Railroad's Boon" by Eric Lipton.

Referendum on how to elect United Kingdom House of Commons

The United Kingdom had the referendum on "alternative vote" system for its House of Commons (parliamentary) elections. They voted resoundingly no. If passed, there would be multi-member districts, with alternative voting, or ranked ballot, to choose who would represent each district. The referendum vote was part of the agreement to form a coalition between the Conservatives and Liberal Democrats.

There was discussion of having a threshold that fourty percent turn out would be needed to pass the referendum.

The Green Party of England Wales is in favor of a proportional vote. They believed that the alternative vote system in the referendum would be a step in the right direction. And this illustrates that we should have several possibilities in a referendum. In this case that would include the Alternative Vote proposed, Proportional Voting, and the Status Quo.

"At a March 2011 Voting Power in Practice annual workshop, held at the London School of Economics (LSE), 22 voting theory specialists voted to select the "best voting procedure" to elect a candidate from a selection of three or more. First past the post received no votes, compared to 10 for AV, although another system, Approval Voting (not on offer in this referendum), received 15 votes.[106]

By the way the Yes campaign outspent the No campaign three to two.

Thanksgiving Thoughtful Thursday, More on Wally Smith and Voting Systems

I had some more thoughts on Dr. Smith's work on Range Voting, or more precisely:

As this is the first Thoughtful Thursday that will be on Thanksgiving, I close with a thanks to some of the wonderful people have explored the ideas of democracy. Political scientists study Locke but do not study Rosseua. I greatly enjoyed Dr. Smith's observations on the probabilities that face a single voter in an election, even a simple binary choice.

1. One goes into a voting booth. What are the odds that your vote will make a difference--that A would have won except for your vote for B. It is 3/sqrt(8*pi*V) where V is the number of voters. If there are a million voters, it one out 1671. Not bad. But this assumes that the poll says the election is a virtual dead heat. That every other voter is as likely to prefer A to B as the other way around, or it is simply "too close to call."
2. But many elections are that close. If the pollsters are saying that people are 60% for A and 40% for B, then the chances that your vote for B will make a difference are vanishingly small. (Even for a 51% to 49% case, the chances are about 10⁹⁰)
3. If we did not have any idea what other people thought--your electiont ou was too small to attract the interest of pollsters, then the odds that your vote would have an effect would be 1/V or (1/2V), depending upon whether V is even or odd. Thus, in our small-town Alderman election with a 1000 people, we would have about a one in 1500 chance of who votes.

Dr. Smith, with his wonderful wry humor, points out that in most elections it is not worth the voter's time to vote as their vote will never matter. And in spite of the hand-wringing of people complaining about voter apathy and lack of turn out, lots of people do vote. But on the other hand, people generally don't "waste their vote" on third party candidates that have even less of a chance than A or B. I can understand people not voting for Nader in the election of Bush vs. Gore, where it was close. But in the election of McCain vs. Obama, where it was clear who was going to win the Presidency, why did we not see more small party voters. As Dr. Smith pointed out that "rational voter" arguments should be given as much credit as most economists talking about a rational homo economicus.

The latter is the key assumption in Dr. Smith's work on Range Voting. Each voter looks at the poll data, and looks at the winner and closest runner up. Then,the voter decides which vote under the voting system, will he be most likely to affect.

And he gets the following algorithms for the Borda vote (a voter ranks the candidates adn the winner gets the sum of the ranks) and range voting.

Borda:: Look at the top two candidates in the polls. Award c votes to your favore. Award 0 votes to your second favorite. Now look at the third most likely to win (from poll data), if you think they are better than the average of the two previous candidates, give them c-2 votes. Otherwise give them 2 votes.

Range: Assume the maximum range you can assign is +1 and the minimum is -1 in this election. Go to the top two candidates, most likely to win--call them A and B. Decide which one you like the best out of those two, the lesser of two evils. Give them +1 to your favorite candidate and -1 to the worse of the two evils. Consult the poll data again and go to the third most likely to win. Call them C Give +1 if that candidates is better than the the average of candidates A and B, -1 otherwise. Then in deciding among the fourth most likely to win, if you like them better than the average of A, B and C, give them +1 , otherwise -1. Dr. Smith calls this generalization the Moving Average Strategy

Dr. Smith tries thirty voting system/strategy pairs. but all the strategic voting possibilities are individual strategies.

Let's say seven percent of the population follows the edicts of Demagogue C. the demagouge has considerable resources and hires computer boffins to determine the best strategic choice. Demagouge says give the vector <0.3,0.2, 0.8, 0.1> In a game theory setting, there might be another demagouge or interest group followed by five per cent that say give the vector< 0.6, 0.2,0.3,0.7> The other 88% are honest. Dr. Smith mentions the issue of allowing the honest voters to be honest which range voting does, and even ten percent honest voters will give better results for society than if everyone is strategic.

Coalitions are important. The wonderful paper of Vinent Conitzy, Tuomas Sandholm and Jerome Lang in Journal of Acm, volume 54, Issue Three discusses these--a topic for another Thoughtful Thursday. And as Dr. Conitzy pointed out, coalitions are weighted electoins. We may have these in shareholder elections where each vote is weighted by the number of shares that one has.

Thus, we should simulate it as a game. This means that each voter considers more possibilities than that given by the affine space and whether it makes sense to only look at the top two candidates in the polls.

I raise a possibility for elections to bodies like the house or Senate. The election is for m candidates over the n fielded. Each of the m winners are weighted by the number of votes they get. So in the Senatorial electon for State S, assume the Republican candiate, R gets 73% of the vote and the DemocratD gets 23% of the vote. There are two possibilities. Unlike the United States current system, the senators from each State are elected at the same time. R gets 1.46 votes and D gets 0.46 votes in the Sentate. The State loses 0.08 votes (for the minor parties). An alternative system which would be kinder to those voting for minor parties would be dividing by the number of votes for the top two candidates. Thus, here R would get 1.52 votes and B would get 0.48 votes so S would not lose a vote.

We should be thankful for the power of simulatoins to look at how large number of voters behavior under various models, and various possible voting systems. Dr. Smith is one such example. We should be thankful for the theoretical models that tells us that it is impossible to create elections and designing systeems that have certain properties. We should be thankful that there have been some trials of particapatory approaches, most notably Switzerland for referenda and cantonal democracy, Participatory Budgeting most notably in Brazil and to a lesser extent in south America, and Athenian Democracy And we should be thankful that somebody has asked in a survey-kind of way about participatory and direct democracy.

http://www.blogger.com/post-create.g?blogID=1223917131662253173#

Wally Smith on Range Voting, Thoughtful Thursday

Range Votting by Warren D. Smith (2004)

Dr Smith identified a class of voting systems where each voter is asked to send back a vector (one number per candidate). The vectors are summed. The candidate whose corresponding number is largest wins.

Many of the voting systems others have discussed are of this category. They each restrict what kind of vector get sent back. Assume, there are three candidates, B, N and G

In conventional voting, each voter simply sends back a one for a single candidate. That is each person has to vote for either B, N and G. thus, we may have the votes

	B	N	G
	1	0	0
	1	0	0
	0	1	0
	0	0	1
	0	0	1
	1	0	0
SUM	3	1	2

Here the winner is B with three votes. Conventional voting allows a vote to be split. There have been several elections where write-in candidates won or split the vote, not just the recent Alaska Senatorial election. IN 1836, the Whigs ran two candidates including Benjamin Harrison for President in a bald-faced but unsuccessful attempt to split the vote. Of course Benjamin Harrison was elected President in 1840 but was to die shortly thereafter.

Then, there is approval voting. Here, each vector is still limited to zeros and ones. However, we allow the voter to enter as many one's as they care to. In the above election, we might have.

	B	N	G
	1	0	0
	1	1	0
	0	1	0
	0	0	1
	0	1	1
	1	1	0
SUM	3	4	2

Here N might have been the second choice of many voters. The approval voting system seems to give a better result. There was a book on approval voting by Dr. Steven Brams and Peter Fishburn, which I will review in a later Thoughtful Thursday.

Then, there is the Borda voting, where each person gives a rank ordering. And we count a first place as one more than a second-place vote. In a three-way election, we will have the numbers zero, one and two with two going to our first choice.;

	B	N	G
	2	0	1
	0	1	2
	0	1	2
	2	1	0
	2	1	1
	0	1	2
SUM	6	5	7

Here, G wins, even though N is practically everybody's second choice.

Range voting gives everybody the most expressiveness. Everyone can put any number between zero and one. (Actually, one can set up range voting with any defined range, say zero to ten like in the Olympics.) Question for the reader--why don't we allow to the voter to put any number without restricting them to a range.

There are other voting systems that one can use. However, they have the disadvantage as the algorithm has to store all the votes. The above types of systems which Dr. Smith calls COAF total, can just work with the totals. I wrote about some of them earlier. Some of them take exponential computer time just to find out who won. Also, each voting machine has to send all the votes to the main office so it can find out the winner. COAF systems are better, the voting machine can send the totals for each candidate to the central machine. That would add the subtotals to find out who won.

Range voting gets out of a lot of the paradoxes and problems in voting theorems. Both Arrow and Gibbard assumed that voters have to give a ranking. In range-voting, each voter provides real numbers.

I have seen several descriptions of Arrow's famous impossibility theorem. I like Dr. Smith's explanation the best (which he attributes to Dr. Fishburn). Each voter gives a ranking of all the voters. My job as a programmer is to write a program that takes the set of ranks and generates a ranking of the candidates. (Of course, in an election for a single senator or governor, we only need to know who won, we don't need to know who the first loser is.) I can write the program anyway I want, but I have to obey the following rules. Arrow also assumed that I have a finite number of voters. (Of course, I question whether the thing might go away with a huge number of voters and) where the probability of a manipulation goes down with the cube of the number of voters.)

In any event, I cannot write an algorithm that fulfills all of these conditions.

1. There is a finite number of voters--obviously. in an election with three (or more) candidates.
2. If all voters agree than one candidate is better than the other will that candidate come out ahead
3. Let there be two sets of V voters each and we run the algorithm in (two parallel universities). Only one voter differs between the two universes. However, they both rank candidates B more than G but rearrange their choices for other candiates. The algorithm should both rank B more than G (or the other way around). This is that the final result should not be affected by how voters behave on irrelevant alternatives. Thus if B wins, if everyone rearranged their choices ranked beledow B, it shouldn't change the fact that B has won. (I have seen some argue that this is not an important criteria.)
4. We also don't allow me to write a dictator solution. That is, I can't just copy one person's choices and ignore everyone else's choices.

Dr. Smith programmed what I would consider the obvious simulation. Some voters are honest. That is they simply send in their utility. Others try to game the system. Dr. Smith calls them rational. They are simply the people who will vote the lesser of two evils. That is those who would prefer N to win but who look at the polls would vote for B or G.

He generated random sets of preferences for candidates. Then he simulates each of them and see how preferred the candidates for each voting system. The honest voters vote their preference. The dishonest (or "rational") voters look at the polling data and vote the way that they think will give them the best possible candidate. (Dr. Smith also includes some nice results for the probability that one's vote will affect the outcome for various models.)

Dr. Smith tried 144 scenarios and in all of them range voting was the one that selected a candidate that made people, on average, the happiest. (I should add that Dr. Smith's papers on voting system are full of wonderful details and arguments and are a joy to read. I urge all to go to his home page and read his political science papers--he also writes papers on a wide variety of topics unrelated to politics.)

Thoughtful Thursday, Slater and Kemeny Voting Systems

Computing Slater Rankings Using Similarities Among Candidates

by Vincent Conitzer, Electroic Commerce 2006 (Search google.com or citeseerx.ist.psu.edu or scholar.google.com to find the full text of this article.)

As Dr. Connitzer wisely reminds us, the Slater index and Kemeny index are different but related. Let's say every voter gives us their preferences or rankings. Maybe the faculty in a department gives us their ranking of preferences for incoming graduate students. How do we get a ranking for every alternative. A Slater index gives us a ranking for the set where the least number of pairwise elections would be wrong.

We know from Arrow theory that one cannot find a reasonable algorithm to combine the rankings. One of the problems is that a mechanism might be disturbed by an irrelevant alternative. Assume that A wins an election against B, we throw in a candidate Q which everyone dislikes compared to A and B. Then, adding Q or deleting to the list of alternatives should not change whether A or B would win.

20%	20%	40%	20%
C	A	D	A
A	B	B	V
B	D	A	w
Q	Q	Q	B
V	V	V	Q

If A and B had a pairwise election, in the above example, A would win. Any ranking should hopefully have A above B but with Condorcet Paradox conditions, that may not be true. That is the final ranking might have B above A.

The Slater index just adds that ranking a blech factor of negative one with 40% preferring that to the more preferred A above B. If it rated V above Q, that would also be a blech factor negative one, even though only twenty percent would like that bad ranking. A Kemeny index looks at how many people dislike a combination. In the above case, the ranking would get a blech factor of 60% and the second a blech factor of 80%. The goal of both the Slater or Kemeny methods is to reduce the "blech" factor for the number of bad comparisons.

Unfortunately, finding the best ranking in either categorization is NP complete to evaluate. That is they are NP complete to find out what the best ranking would be.

Dr. Connitzer found a good way to compute the best ranking, by finding groups of candidates that can be treated the same for all other candidates, "similar" candidates. Example: A B C D E F G H I J are running.

A defeats E
A defeats F
B defeats E
B defeats F
C defeats E
C defeats F
D defeats E
D defeats F

E defeats G
F defeats G
E defeats H
F defeats H
E defeats I
F defeats I
E defeats J
F defeats J

Dr. Conitzer's would find that E and F are similar. He finds a hierarchy structure of sets and subsets thereof where each level in the hierarchy is a similarity set.

So what? If we have thirty candidates--they could be alternatives in a referendum, with ten issues and 191 voters, his algorithm can find the ranking instantaneously, while other algorithms take fourty seconds or so. And it finds a solution when other cannot.

Now this doesn't handle millions of voters--should we use some sort of approximation?

Improved Bounds for Computing Kemeny Rankings

Vincent Conitzer, Andrew Davenport, Jayant Kalagnanam.

Assume there is an election between two alternatives, A and B. The voters can only tell which is better or more correct with a probability of slightly above 50%. Each voter votes for the one that seems the best to them. We saw that if one simply takes the majority, there is a very high likelihood--in reasonable sized electorates, of getting the correct answer or best alternative. This is Condorcet's theorem.

But what if there are dozens of alternatives. It turns out that the Kemeny method would give us the best answer, and each voter had an imperfect idea of what was the best decision. And other voting systems correspond to other models, which is a different paper and a later Thoughtful Thursday.

Of course, there is no reliable way to solve large instances of these. Dr. Connitzer raised the issue of approximations to the Kemeny method--but is that what people were promised. We have seen very close elections, and certainly to have the result be an approximation that could be wrong. Dr. Connitzer developed algorithms to compute the Kemeny method. I won't give the detailed description because I doubt that the readers are interested and if they are, his article describes it far better than I could. But three idea of operations research/computer science are important

1. graph theory
2. linear programming
3. integer programming

Many other techniques in social choice theory represent elections as a graph. The nodes are the candidates and the edges represent the number of votes in a pairwise election. If A would beat b by 32 votes, then Dr. Connitzer's graph would have an arrow from A to B with a 32 on it. The linear programming relaxation has less than a one percent deviation from optimality which is measured by optiamlity. And if most people agree on an order, e. g., the Nazi Party candidate is not wanted, that improves dramatically the ability to find a good ranking. That seems good, but what if an electorate is highly polarized, say between socialized medicine and no government intervention. One interesting study would be to look at a population where there are two consensuses on very different formulations.

An interesting idea would be that after an election, one could have a competition to determine the optimal Kemeny ranking. Different groups of computing scientists could produce a ranking and its Kemeny distance. (It is very easy to verify the Kemeny distance of a given ranking.) The ranking with the minimum Kemeny distance would be the winner. Thus, an agrieved group who narrily lost an election could pay for supercomputer time to try and find a better ranking that hopefully would get what they wanted. One could have some sort of prize for the team of operations researchers and programmers that found a winner.

As I believe I mentioned, if there are thousands of alternatives, e. g. tax codes with slightly different structures, each voter would vote on a subset of alternatives. Drs. Kenyon-Mathieu and Schudy spoke about this in their article on "How to Rank with Few Errors" where they said "In statistics and psychology, one motivation is ranking by paired comparisons: here, you wish to sort some set by some objective but you do not have access to the objective, only a way to compare a pair and see which is better; for example, determining people's preferences for types of food" or perhaps preference for tax code. (I will Thoughtful Thursday this material here.) These would be combined in the same manner and described here as if each voter gave a full preference order.