Mathematicians: Elections Flawed 752
Nader-licious writes "Science News Online reports: 'With recent reports of malfunctioning voter machines and uncounted votes during primaries in Florida, Maryland, and elsewhere, reformers are once again clamoring for extensive changes. But while attention is focused on these familiar irregularities, a much more serious problem is being neglected: the fundamental flaws of the voting procedure itself. Mathematics are shedding light on questions about how well different voting procedures capture the will of the voters.' The verdict: the U.S. system might be the worst of the lot."
Also a good source (Score:4, Informative)
biggest problem (Score:5, Informative)
Re:Absolutely wrong. (Score:5, Informative)
Re:biggest problem (Score:5, Informative)
Re:We may not have a lot of people voting (Score:1, Informative)
Despite the philosophical arguments for/against compulsory voting, note that "punished for not voting" generally means a token fine and that's it; the system of compulsory voting obviously isn't a problem for the majority of the population otherwise you'd hear more complaints about it during each election.
As for calling yourself "free" or not, the United States is the most hypocritical in that regard - the reality is there is no such thing as a totally "free" nation on Earth; every nation we refer to as being "free" is just some variation of a democracy with different degrees of governmental intrusion (read, laws/restrictions). Think about it - the United States is the one which claims to be "free" (not Australia - we don't have any songs claiming to be "home/land of the free"), yet right here on Slashdot you see constant complaints by Americans about the level of legal intrusion either in or potentially in their lives.
I don't even know where to begin with this notion of Australia having "some of the most Big Brother-ish laws on the planet" - talk about rampant paranoia. Have you even read some of the laws in the United States or some European countries?
Sheesh...
Re:The system in Australia (Score:1, Informative)
Perfect example - the recent Cunningham by-election here in NSW; the incumbent member/party (Labor, one of the major Federal options) was kicked out by a member of the Greens (generally a minority party at the Federal level). This has now had two outcomes:
Re:[you are]Absolutely wrong. (Score:2, Informative)
The founding fathers were concerned with creating a country of thirteen colonies that did not trust each other, did not communicate with each other, and were most of the time attempting to jockey for unequal representation. See the debates over the resulting house/senate compromise. The founding fathers, in fact, creating a system in which the president was specifically not chosen in a popular election.
There is nothing in original constitution that says the election of the president requires a popular vote. The relevant text, Article II, Section 1, Clause 2, is
Clause 2: Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector.
In other words, the state can pretty much choose electors as they wish, and further text indicates that electors can vote as they wish. Furthermore, it is argued that the populous would not even have to be aware of a presidential candidate. The electors would choose the best man for the job.
This system rapidly evolved to a system of somewhat popular vote, in which most of the electors were chosen by the people, and the electors would probably vote for a specific candidate. By the mid 19th century the few people who were allowed to vote in general were also allowed to vote on the president.
Jusy my two cents.
Re:Absolutely wrong. (Score:5, Informative)
Count the electoral college votes in Montana compared with Florida, NY, Texas, California... places with much higher populations.
Then tell me how Montana gets a bigger share, somehow.
Montana population: 904,000; electors: 3; Voters per elector: 300,000
California population: 34,000,000; electors: 54; Voters per elector: 629000
Montana: one man, two votes. And Montana is not the only state with excessive representation per voter. It adds up.
Re:The system won't change (Score:3, Informative)
- Point of education for you: Nazis were not right-wing... the name of the party (translated from German obviously), which was originally NDSAP, is "National Socialist Democratic Worker's Party". That word "socialist" and the phrase "worker's party" are big clues - the Nazis were hard-core leftists; they took over many companies and tightly regulated everything. That is not the right-wing philosophy of laissez-faire and caveat emptor.
I assume that your "NDSAP" is a typo - it was actually "NSDAP", standing for Nationalsozialistische Deutsche Arbeiterpartei, which translates to National Socialist German Workers Party (the word "democratic" does not appear).This is a very commonly made error, possibly because the leftist media would prefer to put known bad guys in the other column.
They were a totalitarian regime, i.e. a dictatorship / oligarchy, in which many free-wheeling capitalists got very rich, and in which the workers were as fucked as in any other system other than perhaps China (where they are fucked for other reasons).
I am aware that the word "socialist" is part of the acronym "NSDAP" - put please don't be bamboozled into believing that that is what they actually were. As you might have gathered from my post, I was expressedly writing about the one-dimensional political spectrum on which, alas, nazis figure on the right-handed edge. If you want to talk / learn about multi-dimensional models (e.g. socal-economic split), please log in and we can continue from there.
I shall now stop feeding the troll (after having invoked Godwin. Sigh).
The article ignored the best method (Score:2, Informative)
and overplayed what is arguably the worst -- instant runoff voting (IRV), which not only has the ability to lead to more counterintuitive situations than plurality voting, but also becomes very complex to manage for large elections, because ballots are not "summable". You can't add up all the votes from one voting precinct and send a total on to the next tier up (ultimately you do want to collect all of the physical ballots together, but summability allows decentralized counting for faster results).
But the article completely ignored the Condorcet voting method, which is pretty universally considered to be the best system from a technical point of view. Like IRV and Borda, Condorcet voting asks voters to rank their choices, which is very important because it allows a voter's entire set of preferences to be applied, but unlike them it has far better mathematical properties (mainly because it "discards" almost *no* information from the ballots); is much more "stable" in the sense that changes to votes don't do counterintuitive things; manages to satisfy a slightly relaxed version of Arrow's criteria, which no other voting system can do; and is "summable".
In fact, it's quite arguable that Arrow's criteria were overstated and that the slight weakening of one of his axioms is correct, even though it destroys his proof. Thus it's possible there *is* a perfect voting system, and, arguably Condorcet is it.
Condorcet's clever idea was "pairwise" evaluation. When you only have two candidates, simple majority is a perfect system, so Condorcet applied majority voting to multiple candidates by just taking them two at a time. Since each voter ranks all of the candidates(*), each ballot expresses a choice about any pair of candidates, and you can easily tally up the public's actual preference between that pair.
If one of the candidates is preferred over each of his opponents, then that candidate is the winner, which is very logical if you think about it. It's easy to show that this will happen most of the time, the only time it won't happen is in a three or more-way race where the candidates are all fairly close and where the electorate is seriously divided. What happens is you get a "cycle".
For example, suppose you have three candidates, A, B and C and suppose a majority of the voters ranked A over B, a majority ranked B over C and a majority ranked C over A. Mathematicians have devised some moderately complex but very accurate ways of resolving such issues, basically by looking at how badly the candidates were beaten in their losses. The result is a very stable, very predictable system that accurately reflects the electorate's will and pretty much completely eliminates any possibility of successfully "gaming" the system by casting an insincere vote.
If you'd like to read more about Condorcet and a technical evaluation of the various methods, look here [electionmethods.org]. If you'd like to play with it a bit, I have a Java implementation that you can find here [willden.org]. It's very rough, since I just hacked it together a couple of days ago to evaluate votes for a new name for a SCUBA diving club I'm involved in, but it works pretty well. Just make a file called "rawballots.txt" that contains one ballot per line, with the candidates listed in order, separated by commas (there's a sample on the web site), place the file in the same directory as Condorcet.java, and compile and run (javac Condorcet.java; java Condorcet). My code also abuses the Condorcet system a little by trying to construct a complete ranking of all candidates rather than just finding the winner (it does this by finding a winner, then adjusting the defeats matrix to make him a loser, then finding another winner, until all candidates have "won").
(*)It actually isn't necessary for every voter to rank every candidate. Essentially, any candidates a voter chooses to leave off the ballot are considered as ranked equally and below all of the candidates that were listed. For example, if there are candidates A through E, and I cast a ballot like:
A,B,C
That means I prefer A over everyone, B over C-E, C over D and E and I don't have a preference between D and E.
Actually, although it would probably make voting interfaces to complicated, the method even allows me to express the fact that I don't have a preference between higher-ranked candidates. Something like:
A, (B|C), D
Would mean I like A over everyone, prefer either B or C over D or E, and prefer D over E.
When we're figuring out who won in the pairwise election between B and C, this ballot is a "tie" and effectively doesn't give a vote to either. When counting up the election between B or D and any of the other candidates, however, this ballot expresses a preference.
Re:The system in Australia (Score:1, Informative)
There was little 'red and blue', mostly purple (Score:3, Informative)
This myth is thouroughly debunked here: Reddish Purple vs. Bluish Purple [crummy.com] Fact is, if you look at the actual per-person vote, the country is not a "sea of red with islands of blue", it is instead varying shades of purple when each blue and red vote is counted.
Further, with the archaic electoral system, persons in small states votes count many times more than individuals in large state's. If the USSC was really looking for a violation of the 14th A, they could easily find in an electoral system that makes some folks votes count far more than others based on their location!
PS, It fully borders on sad to see the "red v. blue" myth still being faithfully repeated by the right wing, esp. in a
Re:The Us Presidency is a two-turn election (Score:5, Informative)
1) those aren't legally a part of the election
2) who can vote in them is restricted in most (if not all) states.
3) who can participate as a candidate is pre-selected by the party apparatus.
So they don't qualify either.
They left out Condorcet schemes (Score:2, Informative)
Why do we need a new Single Winner Election Method?
When minority candidates do run in single winner elections, they are criticized for the spoiler effect they may have.
Typical Spoiler Effect: (Note these examples are speculative on voters second and third choices, though the percentages on their first choice are accurate
1992:
43 Clinton, Bush, Perot
37.5 Bush, Perot, Clinton
15 Perot, Bush, Clinton
3.9 Perot, Clinton, Bush
2000:
47.9 Bush, Gore, Nader
48.4 Gore, Nader, Bush
2.7 Nader, Gore, Bush
Potential Solution - Voting Schemes that allow each voter to rank their preferences.
Caveat: Kenneth J. Arrow showed in 1951 (Nobel Prize in 1972) that reasonable criteria for a voting scheme are unachievable:
1) Let each voter rank all candidates in order of preference.
2) Form an overall ranking from the data above such that: (Note: in a single winner, only the first name on the list matters)
a) if voters prefer A to B, then A should rank higher than B in the overall ranking,
b) introducing another candidate into the election should not change the winner, unless it is the new candidate who wins.
It can be shown that no overall ranking scheme exists (assuming there is more than one voter).
Nevertheless, it is possible to relax criteria 2b to get solutions that many people think are better than plurality.
Scheme 1. Instant Runoff Voting (IRV)
If there is no one with more than 50% of the first place votes, the person with the least first place votes is dropped and the second place votes from all the ballots picking that person are then apportioned to the remaining candidates. Repeat as necessary.
Scheme 2. Condorcet voting schemes (my preferred choice)
Condorcet, a French philosopher, formulated the following method around 1785: Form a matrix of all possible pair-wise elections and fill it according to each ranked ballot. If there is one candidate who wins against all others, this is the (Condorcet) winner.
Example: Hypothetical election where Nader gets enough support to knock Gore out in the first round of IRV.
# Ballot
4 B G N (i.e. 4 voters out of 9 prefer Bush over Gore over Nader)
3 N G B
1 G N B
1 G B N
wins)
Plurality: Bush clearly wins (4 to 3)
IRV (after one round): (Bush wins again, 5 to 4)
Condorcet Voting Matrix (row preferred to column)
B G N
B X 4 5
G 5 X 6
N 4 3 X
Gore now wins since he is preferred over Bush and over Nader in separate pairwise elections. Doesn't it sound more logical that he should be elected in this case? There is a benefit of Condorcet schemes over IRV that may not be apparent from an example with only 3 candidates - statistics from a precinct are easily tallied and presented by the above matrix. With IRV, every permutation that arises must be tallied - with 20 candidates, this could be quite large.
2b. What if there is no Condorcet Winner?
Find the Smith set where each candidate in the set wins against any candidate not in the set (could be everyone). Of course the winner should be chosen from the Smith set. There are several ways to do this, but the simplest to describe is Condorcet's original method: Form a ranked list of the margins of defeat for all contests within in the Smith set (e.g. in a race with 4 candidates A, B, C, D):
D/B (60)
B/C (50)
A/B (40)
C/A (30)
C/D (25)
D/A (20)
Then eliminate the lowest contest on the list from consideration and check to see if there is now a Condorcet winner. Repeat as necessary. (e.g. If D/A is eliminated, no one is undefeated. But after the race C/D is eliminated, D is now the undefeated winner).
Conclusion
San Francisco passed IRV (via referenda, starts in Nov 2003), so change is possible. These schemes may sound more complicated than what we have, but they are more fair, computers can do the work, and they might even eliminate primary elections.
References
condorcet.org and electionmethods.org (very thorough coverage of the details of Condorcet methods), outlander.com/condorcet (allows you to vote in 2000 and 2004 elections and see results), fairvote.org (advocates the IRV method), www.idea.int (lots of statistics on US and international elections), civilrights.org (search for "Florida" to find stories on voting rights problems).
Re:Absolutely wrong. (Score:3, Informative)
There is similar textual data at this link [taxfoundation.org], which compares the 1990 data to the 2000 data.
One method ominously absent (Score:2, Informative)
For those not farmiliar with it, the Condorcet method works roughly like this. Voters rank each candidate. If one candidate wins a majority of the vote in every head-to-head pairing they belong to, they win (i.e. A is ahead of B in 65% of ballots, ahead of C in 90% of ballots, and ahead of D in 51% of ballots). If no candidate win every head to head matchup, there are a couple of methods for deciding the winner that give roughly equal results. Basically the winner is the candidate who wins the most head-to-head matchups between candidates that win at least one head-to-head matchup. A complete description of the Condorcet method along with comparisions to other methods can be found at electionmethods.org [electionmethods.org].
The only real drawback to the Condorcet system is its complexity, both in that voters must rank every candidate and that the methods used to determine the winner in close races is difficult to understand. Personally I like methods that require voters to understand all of the candidates, so I do not think the ranking process is a drawback.
I also thought that the article failed to mention a serious fault with the Borda count. By allowing the candidate rankings to count as points rather than as head-to-head matchups, voters are encouraged to place viable second best choices last to improve the standing of the first place candidate. In the Condorcet system there is no advantage to this, ranking candidate B second or tenth makes no difference if the race comes down to A vs. B if A is ranked first on your ballot, A wins the head-to head matchup the same either way. In this manner the Condorcet method is the only method I know of that truly makes the voter vote their conscience, rather than voting strategically to elect the lesser of evils (e.g. voting for Gore when you really like Nader but really hate Bush). Instant runoff has the right idea in this sense but is fundamentally flawed, as the article states due to an increase in support for a candidate possibly causing that candidate to lose.
Re:The system won't change (Score:2, Informative)