Wednesday, November 17, 2004
The Candidate's Dilemma
“We the People.” We’ve all read those words. They form the opening statement of the Constitution, the document that gave birth to the United States of America. The familiarity of the phrase has had the unfortunate effect of diluting its power. It is striking that, in constructing a new nation, the Framers of the Constitution were careful to identify the source of governmental power in the first line of the new government’s blueprint. The People are the authors of the Constitution, and the People are the source of the United States government’s power. After generations of increasing centralization of government power and a trend towards paternalistic socialism, Americans have largely forgotten that it is they, and not their elected officials, who rule. We have given too much authority and bestowed too much trust in the officials of our federal government. The imbalance of power favoring the government is dangerous for many reasons, but recent events have highlighted the danger such an imbalance might pose to the very foundation of our democracy by attacking one of its most vulnerable points: the electoral process.
The events of the recent presidential election could aptly be described as the proverbial “emotional roller coaster.” Politicos on both sides of the aisle likely experienced dramatic swings in their respective states of mind over the course of election Tuesday. Early exit polls showed a commanding lead for John Kerry. Later exit polls verified the early poll results, and it looked like Kerry would win in a landslide. Approximately six hours after the final exit poll results were released, a domino string of news networks called the election for George W. Bush.
The exit polls were wrong – uniformly wrong. How could this have happened? The first – and for most voters and commentators, the final – instinct would be to assume that the exit polls were simply inaccurate enough that disagreement with the final vote counts was not unexpected. That this view dominated the media and voter base is obvious from the startling silence on the issue. Only one mainstream media source, Keith Olberman on MSNBC, has commented on the issue. See http://msnbc.msn.com/id/6210240/ However, the work of at least one professional statistician calls this summary dismissal of the exit poll accuracy into question. According to Dr. David Anick, a former professor of mathematics at the Massachusetts Institute of Technology, the odds that the final vote tallies would differ from the results of the final exit polls by 4.15 points* is 1 in 50,000. See http://www.bluelemur.com/index.php?p=405 In other words, given the exit poll data, there was only a 0.002% chance that Bush could have legitimately “gained” as much ground as he apparently did. While a showing of extreme improbability is not tantamount to a showing of foul play, the accomplishment of such an amazingly improbable act generally inspires reasonable men to seek for evidence of human design. The reason is simple: the improbable is much more probable when human interference is involved. But, if there was fraud, how was it accomplished?
A stream of stories detailing purported incidents of voter fraud followed immediately after the election. Much of it was anecdotal – someone in Florida found a pile of ballots in the trash, boxes of ballots were destroyed in transit, voters in economically depressed districts were intimidated, etc. While these stories are disturbing, their veracity is too uncertain to warrant serious concern. However, at least one study, using official election data from the Florida Secretary of State’s office, produced empirical evidence indicating possible voter fraud. The study, available at http://ustogether.org/election04/FloridaDataStats.htm and http://ustogether.org/Florida_Election.htm compared the ratios of registered Democrats and Republicans to the election returns in each Florida county. The results revealed an interesting trend: in counties that utilized computer touch-screen voting machines, the election results closely tracked the party registration data. However, in counties that employed optical scan voting machines, the election results varied dramatically from the party registration figures – each time in favor of the Republicans. The key observation is that the only uniform distinction between those counties that closely tracked the registration data and those that varied wildly – namely, the type of voting machine employed – also neatly divides the counties into two groups based on ease of perpetrating voter fraud. Computer voting machines perform many of their critical operations in a parallel mode, making it quite difficult to doctor the results. However, optical scan machines feed their data back to a centralized Microsoft Windows computer for tallying. At least one author has suggested that these machines may easily be manipulated to distort election results. See http://www.truthout.org/docs_04/110804Z.shtml
At this point, it would be wise to take a step back and clarify my goal in writing this entry. I want to make it perfectly clear that this analysis was not motivated by partisan animosity. In fact, I should point out that the Olberman article cited above highlights potential voter fraud by the Democrats in Ohio. Rather, my intent is to shed light on a pressing issue in American politics: namely, that we the people are running a grave risk in transferring too much of our responsibility to the government. Our nation belongs to us, not the government. If we want to retain our rights, we must be vigilant in guarding the integrity of the voting process. Our voting rights represent the entirety of our collective voice in government; if we lose the right to vote, we lose any control over our national destiny.
As a people, we should be oversensitive to evidence of voter fraud. Humans are generally oversensitive to sensory data indicating the presence of a nearby predator. When we hear a rustling in the bushes, our first thought is to assume agency and investigate. The reason for this is simple: it is far safer to assume danger where there is none than to assume the absence of danger in a perilous situation. The downside to unnecessary investigation and caution is the loss of a small amount of time and effort; the downside to unjustified confidence could be the loss of life and limb. The same logic applies to voter fraud. We should diligently investigate any reasonable accusation of fraud. If no fraud is found, then we have done nothing more than assuage our fears and increase confidence in the election process. However, if fraud is found, then we have a chance to eliminate it and prevent future injustices.
While it is obvious that vigilant investigation of voter fraud is critical, it is not so obvious where the responsibility for conducting such investigations should lie. The purpose of this entry is to argue that it is we the people who must conduct such investigations and oversee elections. It is we who possess the requisite incentives to ensure fair elections; we cannot trust the candidates to self-police, nor can we trust the various departments of government – who are, after all, the employees of the winning candidates – to expose voter fraud. Government officials are inspired by only one goal, the acquisition of power. As such, an interesting dynamic governs the decision to cheat in an election. This dymanic, as it turns out, is very similar to the “prisoner’s dilemma” of economic game theory.
A nice summary of the prisoner’s dilemma is available at http://plato.stanford.edu/entries/game-theory/#PD The dilemma occurs when two individuals (i.e. the “players”) independently make choices that collectively affect the outcome for both players. The prisoner’s dilemma goes like this: two criminals are brought into custody for the same crime. Each is told that he may confess or remain silent. Each is also told that the following possibilities will occur, depending on the answers of both players: (1) if A confesses and B confesses, each will receive 5 years in prison, (2) if A confesses and B remains silent, A will receive 0 years in prison and B will receive 10, (3) if A remains silent and B confesses, A will receive 10 years in prison and B will receive 0, and (4) if A and B both remain silent, each will receive 2 years in prison. The situation may be charted like this, where the numbers in parentheses represent (A’s prison term, B’s prison term) for each set of choices:
Obviously, the globally optimal situation (i.e. the result that would be best for the aggregate of all players involved) would be for both A & B to remain silent. In that case, the total number of years in prison would be 4. In all other cases, the total number of years spent in jail would equal 10. However, the rub of the prisoner’s dilemma is that the globally optimal result will not be the outcome of a game played by rational actors. In fact, the result of such a game will be not only suboptimal in a global sense, but will be one in which each player is worse off than they could be. The reason is that “rational actors” seek, at every decision point, to optimize their own interests.
In this case, regardless whether A chooses to confess or to remain silent, B’s best choice is to confess: if A confesses, B has a choice to confess and take a 5-year term or remain silent and go to jail for 10 years; if A remains silent, B can confess and go free or remain silent and take a 2-year stint up river. In both cases, B’s best option is to confess. Knowing that B will confess (because it is always in his best interest), A must also confess to avoid a 10-year sentence. The result is that both A and B will confess and take 5-year prison terms (this outcome is termed the "Nash equilibrium"). If both had remained silent, each would have received only a 2-year sentence and both would be better off. (NOTE: The preceding discussion provides only a very cursory analysis of the prisoner’s dilemma. Careful study of the link provided above is recommended.)
A similar dilemma is created for politicians running for office. In such a situation, both candidates have a choice: to cheat or not to cheat. For the purposes of simplicity, we will assume that the candidates are able to cheat in a way that is undetectable. This assumption might seem suspect, but the level of sophistication required to deal with a variable probability of detection is beyond the scope of this analysis. Additionally, the assumption may be justified by recognition of the fact that any candidate that cheats and wins will exercise significant authority over those charged with investigating any allegations of fraud. Another assumption made in this analysis is that each candidate cheats equally effectively. It should be noted, however, that both assumptions are irrelevant to the main point. When both are incorporated into the analysis, the result is basically the same.
The dynamics of the candidate’s dilemma may be represented in the following chart, which evaluates the results in terms of the candidates’ probability for election.
The end result of the candidate’s dilemma is that both candidates have an incentive to cheat - even though each candidate's probability for victory is no better if both cheat than it is if neither cheat. Dual cheating is the Nash equilibrium of the candidate's dilemma. This result occurs because, whether the opponent cheats or not, it is too the benefit of each candidate to cheat. For example, whether or not A cheats, B’s best move is always to cheat (and vice-versa). And, thus, political candidates have an incentive to commit voter fraud in their own favor. Perhaps even more importantly, the winner will inevitably have no incentive to investigate allegations of cheating. This is so for two reasons: (1) any effective investigation would likely uncover evidence of his own cheating and (2) he (and his party) is likely to have benefited from the cheating, and thus would be foolish to support the eradication of a useful tool.
The only candidate who might have an incentive to initiate a post-election investigation would be one who did not cheat and, likely, lost. However, at this point the candidate is most likely either a private citizen (and thus, one of the “people” whom I assert bear the burden for investigating voter fraud) or a government official in a lower capacity (i.e. a senator, governor, etc.). Of course, if he is a government official of any capacity, it is possible that he had perpetrated voter fraud to win his election to that post and would thus be unlikely to bite the hand that, at least in one instance, served to feed him.
The sad effect of the candidate’s dilemma emerges when we include a third outcome which represents the “value” of the public’s collective voting rights. In an honest election, the value of the public’s voting rights is at a maximum. But, in a dishonest election, there is little or no value in the right to vote. In such a case, the act of voting is an absurd and meaningless exercise.
The following chart details the candidate’s dilemma with the resulting value of the public’s voting rights included as the third number. We will represent the "value" of voting rights on a 0-10 scale, with 10 representing the highest value.
As the chart shows, in only one outcome - the one in which our votes, and not the cheating of candidates, determines the election's outcome - do the voting rights of the people retain any value. Unfortunately, the "clean election" result is not the Nash equilibrium and is thus unlikely to occur. The inclusion of the value of voters rights has no effect on the candidates' decision whether or not to cheat, because that value is an externality in their decision. In other words, the diminishing value of a vote is a detriment that falls on other people, and not the decision makers. Therefore, the decision makers have no reason to account for it.
The lesson is that the candidates’ incentives guide them towards a set of decisions that renders our voting rights entirely worthless. If we delegate our responsibility to police the voting process in this country to our government, we place our candidates in a situation that rewards their dishonesty and theft of our democratic rights. Thus, it should be clear that, if we the people are to retain our democratic voice, it is we the people who must fight to maintain the integrity of the election process. No one else can be expected to do it for us.
* The “swing” between the final exit poll results and the final election results was 4.15 points, in favor of George W. Bush.
The events of the recent presidential election could aptly be described as the proverbial “emotional roller coaster.” Politicos on both sides of the aisle likely experienced dramatic swings in their respective states of mind over the course of election Tuesday. Early exit polls showed a commanding lead for John Kerry. Later exit polls verified the early poll results, and it looked like Kerry would win in a landslide. Approximately six hours after the final exit poll results were released, a domino string of news networks called the election for George W. Bush.
The exit polls were wrong – uniformly wrong. How could this have happened? The first – and for most voters and commentators, the final – instinct would be to assume that the exit polls were simply inaccurate enough that disagreement with the final vote counts was not unexpected. That this view dominated the media and voter base is obvious from the startling silence on the issue. Only one mainstream media source, Keith Olberman on MSNBC, has commented on the issue. See http://msnbc.msn.com/id/6210240/ However, the work of at least one professional statistician calls this summary dismissal of the exit poll accuracy into question. According to Dr. David Anick, a former professor of mathematics at the Massachusetts Institute of Technology, the odds that the final vote tallies would differ from the results of the final exit polls by 4.15 points* is 1 in 50,000. See http://www.bluelemur.com/index.php?p=405 In other words, given the exit poll data, there was only a 0.002% chance that Bush could have legitimately “gained” as much ground as he apparently did. While a showing of extreme improbability is not tantamount to a showing of foul play, the accomplishment of such an amazingly improbable act generally inspires reasonable men to seek for evidence of human design. The reason is simple: the improbable is much more probable when human interference is involved. But, if there was fraud, how was it accomplished?
A stream of stories detailing purported incidents of voter fraud followed immediately after the election. Much of it was anecdotal – someone in Florida found a pile of ballots in the trash, boxes of ballots were destroyed in transit, voters in economically depressed districts were intimidated, etc. While these stories are disturbing, their veracity is too uncertain to warrant serious concern. However, at least one study, using official election data from the Florida Secretary of State’s office, produced empirical evidence indicating possible voter fraud. The study, available at http://ustogether.org/election04/FloridaDataStats.htm and http://ustogether.org/Florida_Election.htm compared the ratios of registered Democrats and Republicans to the election returns in each Florida county. The results revealed an interesting trend: in counties that utilized computer touch-screen voting machines, the election results closely tracked the party registration data. However, in counties that employed optical scan voting machines, the election results varied dramatically from the party registration figures – each time in favor of the Republicans. The key observation is that the only uniform distinction between those counties that closely tracked the registration data and those that varied wildly – namely, the type of voting machine employed – also neatly divides the counties into two groups based on ease of perpetrating voter fraud. Computer voting machines perform many of their critical operations in a parallel mode, making it quite difficult to doctor the results. However, optical scan machines feed their data back to a centralized Microsoft Windows computer for tallying. At least one author has suggested that these machines may easily be manipulated to distort election results. See http://www.truthout.org/docs_04/110804Z.shtml
At this point, it would be wise to take a step back and clarify my goal in writing this entry. I want to make it perfectly clear that this analysis was not motivated by partisan animosity. In fact, I should point out that the Olberman article cited above highlights potential voter fraud by the Democrats in Ohio. Rather, my intent is to shed light on a pressing issue in American politics: namely, that we the people are running a grave risk in transferring too much of our responsibility to the government. Our nation belongs to us, not the government. If we want to retain our rights, we must be vigilant in guarding the integrity of the voting process. Our voting rights represent the entirety of our collective voice in government; if we lose the right to vote, we lose any control over our national destiny.
As a people, we should be oversensitive to evidence of voter fraud. Humans are generally oversensitive to sensory data indicating the presence of a nearby predator. When we hear a rustling in the bushes, our first thought is to assume agency and investigate. The reason for this is simple: it is far safer to assume danger where there is none than to assume the absence of danger in a perilous situation. The downside to unnecessary investigation and caution is the loss of a small amount of time and effort; the downside to unjustified confidence could be the loss of life and limb. The same logic applies to voter fraud. We should diligently investigate any reasonable accusation of fraud. If no fraud is found, then we have done nothing more than assuage our fears and increase confidence in the election process. However, if fraud is found, then we have a chance to eliminate it and prevent future injustices.
While it is obvious that vigilant investigation of voter fraud is critical, it is not so obvious where the responsibility for conducting such investigations should lie. The purpose of this entry is to argue that it is we the people who must conduct such investigations and oversee elections. It is we who possess the requisite incentives to ensure fair elections; we cannot trust the candidates to self-police, nor can we trust the various departments of government – who are, after all, the employees of the winning candidates – to expose voter fraud. Government officials are inspired by only one goal, the acquisition of power. As such, an interesting dynamic governs the decision to cheat in an election. This dymanic, as it turns out, is very similar to the “prisoner’s dilemma” of economic game theory.
A nice summary of the prisoner’s dilemma is available at http://plato.stanford.edu/entries/game-theory/#PD The dilemma occurs when two individuals (i.e. the “players”) independently make choices that collectively affect the outcome for both players. The prisoner’s dilemma goes like this: two criminals are brought into custody for the same crime. Each is told that he may confess or remain silent. Each is also told that the following possibilities will occur, depending on the answers of both players: (1) if A confesses and B confesses, each will receive 5 years in prison, (2) if A confesses and B remains silent, A will receive 0 years in prison and B will receive 10, (3) if A remains silent and B confesses, A will receive 10 years in prison and B will receive 0, and (4) if A and B both remain silent, each will receive 2 years in prison. The situation may be charted like this, where the numbers in parentheses represent (A’s prison term, B’s prison term) for each set of choices:
| B |
|||
| Confess |
Remain
silent |
||
| A |
Confess |
(5, 5) |
(0, 10) |
| Remain
silent |
(10, 0) |
(2, 2) |
|
Obviously, the globally optimal situation (i.e. the result that would be best for the aggregate of all players involved) would be for both A & B to remain silent. In that case, the total number of years in prison would be 4. In all other cases, the total number of years spent in jail would equal 10. However, the rub of the prisoner’s dilemma is that the globally optimal result will not be the outcome of a game played by rational actors. In fact, the result of such a game will be not only suboptimal in a global sense, but will be one in which each player is worse off than they could be. The reason is that “rational actors” seek, at every decision point, to optimize their own interests.
In this case, regardless whether A chooses to confess or to remain silent, B’s best choice is to confess: if A confesses, B has a choice to confess and take a 5-year term or remain silent and go to jail for 10 years; if A remains silent, B can confess and go free or remain silent and take a 2-year stint up river. In both cases, B’s best option is to confess. Knowing that B will confess (because it is always in his best interest), A must also confess to avoid a 10-year sentence. The result is that both A and B will confess and take 5-year prison terms (this outcome is termed the "Nash equilibrium"). If both had remained silent, each would have received only a 2-year sentence and both would be better off. (NOTE: The preceding discussion provides only a very cursory analysis of the prisoner’s dilemma. Careful study of the link provided above is recommended.)
A similar dilemma is created for politicians running for office. In such a situation, both candidates have a choice: to cheat or not to cheat. For the purposes of simplicity, we will assume that the candidates are able to cheat in a way that is undetectable. This assumption might seem suspect, but the level of sophistication required to deal with a variable probability of detection is beyond the scope of this analysis. Additionally, the assumption may be justified by recognition of the fact that any candidate that cheats and wins will exercise significant authority over those charged with investigating any allegations of fraud. Another assumption made in this analysis is that each candidate cheats equally effectively. It should be noted, however, that both assumptions are irrelevant to the main point. When both are incorporated into the analysis, the result is basically the same.
The dynamics of the candidate’s dilemma may be represented in the following chart, which evaluates the results in terms of the candidates’ probability for election.
| B |
|||
| Cheat |
Not cheat |
||
| A |
Cheat |
(50%, 50%) |
(100%, 0%) |
| Not cheat |
(0%, 100%) |
(50%, 50%) |
|
The end result of the candidate’s dilemma is that both candidates have an incentive to cheat - even though each candidate's probability for victory is no better if both cheat than it is if neither cheat. Dual cheating is the Nash equilibrium of the candidate's dilemma. This result occurs because, whether the opponent cheats or not, it is too the benefit of each candidate to cheat. For example, whether or not A cheats, B’s best move is always to cheat (and vice-versa). And, thus, political candidates have an incentive to commit voter fraud in their own favor. Perhaps even more importantly, the winner will inevitably have no incentive to investigate allegations of cheating. This is so for two reasons: (1) any effective investigation would likely uncover evidence of his own cheating and (2) he (and his party) is likely to have benefited from the cheating, and thus would be foolish to support the eradication of a useful tool.
The only candidate who might have an incentive to initiate a post-election investigation would be one who did not cheat and, likely, lost. However, at this point the candidate is most likely either a private citizen (and thus, one of the “people” whom I assert bear the burden for investigating voter fraud) or a government official in a lower capacity (i.e. a senator, governor, etc.). Of course, if he is a government official of any capacity, it is possible that he had perpetrated voter fraud to win his election to that post and would thus be unlikely to bite the hand that, at least in one instance, served to feed him.
The sad effect of the candidate’s dilemma emerges when we include a third outcome which represents the “value” of the public’s collective voting rights. In an honest election, the value of the public’s voting rights is at a maximum. But, in a dishonest election, there is little or no value in the right to vote. In such a case, the act of voting is an absurd and meaningless exercise.
The following chart details the candidate’s dilemma with the resulting value of the public’s voting rights included as the third number. We will represent the "value" of voting rights on a 0-10 scale, with 10 representing the highest value.
| B |
|||
| Cheat |
Not cheat |
||
| A |
Cheat |
(50%, 50%, 0) |
(100%, 0%, 0) |
| Not cheat |
(0%, 100%, 0) |
(50%, 50%, 10) |
|
As the chart shows, in only one outcome - the one in which our votes, and not the cheating of candidates, determines the election's outcome - do the voting rights of the people retain any value. Unfortunately, the "clean election" result is not the Nash equilibrium and is thus unlikely to occur. The inclusion of the value of voters rights has no effect on the candidates' decision whether or not to cheat, because that value is an externality in their decision. In other words, the diminishing value of a vote is a detriment that falls on other people, and not the decision makers. Therefore, the decision makers have no reason to account for it.
The lesson is that the candidates’ incentives guide them towards a set of decisions that renders our voting rights entirely worthless. If we delegate our responsibility to police the voting process in this country to our government, we place our candidates in a situation that rewards their dishonesty and theft of our democratic rights. Thus, it should be clear that, if we the people are to retain our democratic voice, it is we the people who must fight to maintain the integrity of the election process. No one else can be expected to do it for us.
* The “swing” between the final exit poll results and the final election results was 4.15 points, in favor of George W. Bush.
Comments:
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Brickhorn, I may not often agree with you, but this is very well stated. I'm less inclined to doubt the system, but you logic is very good.
Hornpop
Hornpop
# posted by 
: 10:22 AM
: 10:22 AM
Thanks for the comments. I will say this: all the logic indicates is that SOMEONE needs to be vigilant in investigating voter fraud and that only the voters themselves have the requisite incentives to ensure a diligent investigation.
Bear in mind that my cursory analysis ignored a few complicating factors, such as the emotional drives toward honesty. These emotions are a result of evolution, which has in large part given us the capability for irrational decision making in order to avoid sub-optimal Nash equilibria. For example, the prisoners might both remain silent out of a bond of loyalty. Neither's decision is rational, but both end up better off because of their irrational emotions.
In any case, the simplistic analysis that assumes rational players provides information about the worst-case scenario. In reality, the players probably experience a mixture of rational feelings and irrational emotions (such as honor, integrity, etc.) However, given that it benefits us to be overly skeptical, it is safer to assume the worst case and be wrong than to assume the rosy picture and be wrong. Vigilant investigation into allegations of voter fraud can only result in two outcomes: (a) the allegations were wrong or (b) the allegations were correct. In either case, the outcome is beneficial. In the latter, the new information helps us prevent future voter fraud and in the former, the results of the investigation give us more confidence in our democratic government and the integrity of our governing officials. I hate buzzwords, but it's a win-win situation.
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Bear in mind that my cursory analysis ignored a few complicating factors, such as the emotional drives toward honesty. These emotions are a result of evolution, which has in large part given us the capability for irrational decision making in order to avoid sub-optimal Nash equilibria. For example, the prisoners might both remain silent out of a bond of loyalty. Neither's decision is rational, but both end up better off because of their irrational emotions.
In any case, the simplistic analysis that assumes rational players provides information about the worst-case scenario. In reality, the players probably experience a mixture of rational feelings and irrational emotions (such as honor, integrity, etc.) However, given that it benefits us to be overly skeptical, it is safer to assume the worst case and be wrong than to assume the rosy picture and be wrong. Vigilant investigation into allegations of voter fraud can only result in two outcomes: (a) the allegations were wrong or (b) the allegations were correct. In either case, the outcome is beneficial. In the latter, the new information helps us prevent future voter fraud and in the former, the results of the investigation give us more confidence in our democratic government and the integrity of our governing officials. I hate buzzwords, but it's a win-win situation.
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