The delegation game

Randomization is a standard solution in problems of game theory. In this context, randomization is used to baffle an adversary, who would be able to counter any deterministic strategy (assuming that that strategy was known to her) more effectively than she would be able to counter a randomized strategy. Thus, randomization is a maximin strategy: it guarantees the randomizer the best possible worst-case outcome. Sortition – a randomized strategy for selecting political delegates – can be advocated on similar grounds.

In a standard conception of the problem of selecting delegates, the people can assess the quality of any possible delegate set. They do so and then choose the delegation that maximizes that quality. Thus, in this conception, delegation is a maximization problem.

An alternative conception is one where the quality of potential delegations is difficult to assess. In such a situation, selecting a delegation requires some way to handle the uncertainty. One such way is to assume that even if quality is not observable, an estimate of the quality can be made, and the estimate can then be used instead of the quality itself as an objective for maximization. This setup is theoretically consistent as long as the uncertainty about the quality of delegations is unbiased – i.e., as long as the uncertainly in quality is not correlated with the perception of quality. Corruption, however, is not an unbiased process. As the maxim “power corrupts” reflects, corruption is a dynamic process which depends on many factors, including, significantly, the level of distinction of the person or group in question. A person or group that are perceived as having the highest quality as a potential delegate or delegation could be more susceptible to corruption than a person or group that are perceived as average.

Thus, the process of corruption can be realistically likened to an adversary which counters methods for selecting delegations by corrupting those delegations that are most likely to be selected. This phenomenon may be due to natural tendencies of individuals or groups, or to the existence of true adversaries, i.e., individuals or groups that have an interest in subverting the quality of government and which actively work to corrupt potential delegates. Whatever underlying mechanism is, the outcome is a situation in which perceptions of quality are wholly unreliable – not even as noisy unbiased estimates.

In such a situation, just like in an adversarial game, the safest strategy to pursue is a maximin strategy – i.e., a strategy which guarantees a best worst-case outcome. If corruption affects a subset of the possible delegations, but it is impossible to identify which delegations would be corrupt, then it is most prudent to choose a delegation by randomization, since any deterministic choice makes it possible that the same distinguishing characteristic that is used for selection of the delegates also makes them more susceptible for corruption.

This argument may be used to justify various forms of randomization, depending on various assumptions about the distribution of competence in the population and about the way the process of corruption affects it. At an extreme case, an equal-chance lottery among the entire set of possible delegations minimizes the chance of having a corrupt delegation. Moving away from that extreme, a mechanism in which some groups – that are considered as having very low competence, such as children – are excluded can be considered as aiming at achieving a balance between reducing the chance of corruption while not giving up completely on the application of some judgement of competence. Approaching determinism, a mechanism in which the lottery is limited to some elite group, such as was employed in the city-states of Italy, can still be seen as enjoying some anti-corruption benefits. Weighted lotteries can also be seen as lying on the spectrum between a completely deterministic process and a completely random process.

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21 Responses

  1. I’m not quite sure I follow you. When you say…

    “This setup is theoretically consistent as long as the uncertainty about the quality of delegations is unbiased – i.e., as long as the uncertainly in quality is not correlated with the perception of quality. Corruption, however, is not an unbiased process. As the maxim ‘power corrupts’ reflects, corruption is a dynamic process which depends on many factors, including, significantly, the level of distinction of the person or group in question. A person or group that are perceived as having the highest quality as a potential delegate or delegation could be more susceptible to corruption than a person or group that are perceived as average.”

    …I take you to mean that there is a correlation between perceived qualifications and susceptibility to corruption. This could mean two things. One, people think they’re perceiving qualifications, but they’re not–they’re actually perceiving something irrelevant that’s linked to susceptibility to corruption. That seems wrong, and if jt was true, then the right thing to do would be to ignore people’s perceptions of quality, which weren’t tracking anything good. Alternatively–and I think this is what you mean–they ARE accurately perceiving quality, but quality correlated with susceptibility to corruption. It’s a reasonable possibility–I believe Zakaras quotes Robert Putnam to the effect that the people most qualified to serve the public good often have the least incentive to do so. But then there is a real difference in qualifications–the people aren’t just being stupid about this–it’s just that qualifications bring something else bad with them.

    Your game theory analogy is worth exploring in more detail, but that will have to wait for another post. Remind me, please, if I wind up forgetting about this.

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  2. In considering theories relevant to the support of a sortitionally chosen legislature, what do you think of the relevance of these? Or others?

    Chaos Theory / Fractals / Schrödinger’s Cat / Emergence

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  3. “It guarantees the the best possible worst-case outcome.”

    I think we can do better than that. If one agrees that Condorcet’s theorem can be applied to political decision making (a contested claim) then randomisation would ensure the optimal outcome, so long as the jury is of a sufficient size and the independence criteria are satisfied.

    Some people argue that Condorcet’s theorem is not applicable to politics as there is no “right” answer in this domain, only opinion. I disagree and would cite the Grofman and Feld paper in support, abstract below:

    ===================================
    We identify three basic elements of Rousseau’s theory of the general will: (1) there is a common good; (2) citizens are not always accurate in their judgments about what is in the common good; and (3) when citizens strive to identify the common good and vote in accordance with their perceptions of it, the vote of the Assembly of the People can be taken to be the most reliable means for ascertaining the common good. We then show that Condorcet’s (1785) model of collective judgment shares these assumptions with Rousseau and that understanding the implications of Condorcet’s (1785) “jury theorem” enables us to clarify many of the most obscure aspects of Rousseau’s treatment of the general will, including his discussion of the debilitating effects of factions and his confidence in the ability of the Assembly of the People to discern the general will by means of voting.

    Grofman and Feld, Rousseau’s General Will: A Condorcetian Perspective, American Political Science Review, 82, 2, June 1988

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  4. Keith, I agree that the Condorcet Jury Theorem is relevant. I think, however, that its application is difficult. All it says, after all, is that if every agent is of reasonable competence, and their judgments are independent of each other, then the majority will be highly likely to decide correctly. But if all citizens are equally competent, then ANY selection procedure will produce a legislature capable of deciding effectively, provided that the legislature is large. To get a case for sortition, one would need to show that random selection adds something to the legislature’s composition. (I have a paper in the works investigating the relationship between diversity and collective wisdom.) Anyone interested in seeing a copy should let me know.

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  5. > I take you to mean that there is a correlation between perceived qualifications and susceptibility to corruption.

    While this may be true, I am making a weaker claim – that there is a correlation between perceived qualifications and corruption. It may be true that one of the reasons for the increased corruption is an innate increased susceptibility, but it may be that the it is simply the special circumstances that such people find themselves in that increase corruption.

    To make matters more concrete, let’s imagine a simplified mechanism – one that assumes corruption is caused by the deliberate activities of an adversarial organization. In this mechanism, once the organization identifies a person who is perceived by the public – or that has some chance of being perceived – as being a good candidate, the organization approaches that person and by a combination of promises and threats attempts to convince her to serve the interests of the organization rather than those of the public. The candidate, who is not any more susceptible to corruption than the average person, would sometimes yield and sometimes would not. Those who yield would find their reputation enhanced by the application of various resources and would become well known candidates, while those that do not will not get that support and would very likely remain anonymous.

    I certainly do not believe that “the people most qualified to serve the public good often have the least incentive to do so.” This seems to imply that people who are not corrupt are incompetent – not a view of humanity that I subscribe to. In fact, I think, there are plenty of well qualified people who try their best to serve the public. The problem as I see it is that these people are not in a position of power and therefore cannot turn their well informed, well intentioned ideas into policy.

    > This could mean two things. One, people think they’re perceiving qualifications, but they’re not–they’re actually perceiving something irrelevant that’s linked to susceptibility to corruption. That seems wrong, and if it was true, then the right thing to do would be to ignore people’s perceptions of quality, which weren’t tracking anything good.

    But this is essentially what randomization does – it ignores, or at least attenuates greatly – the various considerations used by people for rating candidates.

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  6. And of course I am interested in your paper, Peter.

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  7. Peter Stone: “But if all citizens are equally competent, then ANY selection procedure will produce a legislature capable of deciding effectively, provided that the legislature is large.”

    The dilemma for political decision-making is the need for representatives (however selected) to combine judgmental competence with the representation of their own and their constituents’ interests. Madison thought that his formula for large electoral constituencies would resolve the dilemma, but failed to anticipate the damage that would be done by partisan forces. This would appear to be an inevitable consequence of preference elections.

    So why would sortition be any different? The Jury Theorem only applies under conditions of independent judgment, which would be easier to achieve with sortition. Although Condorcet argued that his theorem required that jurers should vote on the basis of the general will, rather than their individual preferences, this is not strictly necessary (and is hard to imagine, given our liberal democratic worldview). This is because, as Madison predicted, individual preferences will balance out, so long as they don’t become factious (hence the need for careful institutional design).

    Even Rousseau acknowledged as much:

    “The [general will] looks only to the common interest. The [will of all] looks only to private interest and is only the sum of particular wills: but take away from these same wills the pluses and minuses which cancel each other out and the general will remains as the sum of the differences.” Rousseau, Social Contract (NY: 1984), 76, 2.3.

    Rousseau understood deliberation as the exercise of silent judgment and would have been appalled by the emphasis of modern deliberative democrats on chattering, as this potentially undermines the independence of each member of the legislature. Yet at the same time judgment needs to be informed – hence the need for careful institutional design to reconcile this further dilemma.

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  8. Yoram, if I’m understanding you correctly, then the question of qualifications (perceived or actual) is simply orthogonal to your point. The problem with elections is that there’s no way to hold them without letting people know well in advance who the viable candidates are (obviously). And this makes it possible for special interests to corrupt them. The exact same thing would happen, I presume, if you selected people by lot six months before their terms were supposed to begin. Isn’t the critical factor in your story the advanced warning about who will be taking office? Or is there some other factor at work?

    Keith, it sounds like you want government officials to perform more than one task at once, or rather to satisfy two different criteria at once. The CJT has trouble handling that idea. This may be why I’m having a bit of trouble seeing what you think random selection contributes here. I do agree, however, that it might reduce the danger of dependent opinions, which impedes the CJT.

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  9. “Keith, it sounds like you want government officials to perform more than one task at once.”

    Au contraire. As Madison predicted, that doesn’t work, and that’s why I keep droning on about the need to separate advocacy and judgment — elections for the former and sortition for the latter.

    What I am realistic about is the fact that allotted members will almost certainly judge on the basis of personal/class/economic interests, as opposed to attempting to divine the general will. But, as even Rousseau grudgingly acknowledged, that doesn’t really matter (see quote in my previous post). The all-important thing is to preserve the independent opinion of each allotted member, hence my Rousseau-derived preference for inner (silent) deliberation over the ideal speech situation and other attempts to privilege the production of hot air.

    Keith

    PS I would prefer not to use the term “government official” as that is normally reserved for the executive, not the legislature.

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  10. Yoram: “I am making a weaker claim – that there is a correlation between perceived qualifications and corruption.”

    Assuming this is true (which I don’t), you’re still throwing out the baby (qualifications) with the bathwater (potential corruption). Much safer to fight fire with fire and ensure a wide diversity of qualifications and expert perspectives so that ‘ambition counteracts ambition’ (Fed 10). And, of course, leave the voting to the allotted members who will be able to judge which of the highly-qualified rapscallions is the least mendacious. Excluding the well-qualified sounds too much like Pol Pot for my taste.

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  11. > Isn’t the critical factor in your story the advanced warning about who will be taking office?

    Not really. According to the model that I suggested, it is the distinction itself that is critical, rather than someone knowing the association between the distinction and taking office.

    Say, for example, that sortition is used, but the lottery is secretly rigged so that people friendly to a certain interest are more likely to be selected. Then, despite the fact that the selection bias is unknown to most people (including to the selected themselves), government is corrupt.

    Of course, having a certain distinction known as being associated with taking office helps further solidify the elite status of the distinction and therefore may be a contributing factor in the corruption of the members of that elite.

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  12. Also, just to make things clear regarding the example I gave above in which a corrupting organization is at work: In this case, the advance warning is a necessary but not a sufficient condition for corruption. If, say, the organization is able to corrupt 10% of the people it approaches, then it would have little effect in a sortition based system in which most office holders would remain unaffected, but, through the control of resources needed for mounting electoral campaigns, it could make sure that those 10% that are corrupt would be the ones that become widely known and would thus make the overwhelming majority of office holders.

    [BTW, in case this was not obvious: Any resemblance between the corrupting organization and real life established political parties is wholly deliberate.]

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  13. All the more reason for keeping election and allotment entirely separate: elections (for advocates) can be as corrupt as you like, so long as the final judgment is in the hands of the allotted assembly. Electing office holders is a very bad idea as it ensures neither competence nor impartiality.

    Returning to the legal analogy, everyone knows that advocacy is corrupt, as the more you pay the better the lawyer you get. But the integrity of the jury has to be ensured as its role is impartial judgment.

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  14. I’m still unclear on how the corruption works on your account, Yoram. It’s not simply a matter of certain people being of the type “corrupt”. Rather, corruption is something that gets done to them by special interests (a single special interest, in your stylized story). But what precisely is it that makes it possible for some people but not others to be corrupted? If everyone is equally corruptible, then advanced warning as to who is taking office would be necessary and sufficient for corruption. If it’s not sufficient, then some people must be different from others, and the corruptible type are the ones who get in with advanced warning under elections. But what makes them corruptible?

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  15. Peter,

    > I’m still unclear on how the corruption works on your account

    The mechanism of corruption in the model is unspecified. This lack of specification of the adversarial strategy is a feature which the model shares with the game theory setup. A successful game strategy is one which is able to counter an opponent whose strategy is unknown in advance. If the strategy of the opponent is known, then the game theory setup degenerates into a standard optimization setup.

    The examples that I gave (explicit corruption by an adaptive organization, or a biased lottery) are possible mechanisms of corruption, but should not be taken to indicate that the model assumes those mechanisms. The randomization solution, it is argued, is robust against a wide variety of mechanisms, guaranteeing a good outcome against any of them (i.e., it is a maximin solution).

    In fact, the word “corruption” may be somewhat misleading. The term is used merely to indicate divergence between the policy objectives of a decision maker and those of the population at large. In that sense, any individual is corrupt since any individual would have policy objectives that are to some extent a reflection of the individual’s ideas and interests, which are very likely not to reflect the ideas and interests of the population at large on a wide range of policy areas. A decision making group, however, can be non-corrupt. This is the reason that the model is focused on the corruption of potential delegations (as groups) rather than on the corruption of potential delegates (as individuals).

    > But what precisely is it that makes it possible for some people but not others to be corrupted? If everyone is equally corruptible, then advanced warning as to who is taking office would be necessary and sufficient for corruption.

    Again, we could assume different mechanisms, leading to different answers to this question. Above, I assumed that there is some innate property of “corruptibility” that afflicts 10% of the population. I also assumed that this innate property is not a-priori correlated with any other attribute (e.g., competence or perception of competence). In this scenario, it is the selection process of the corruptible among those with the potential for a compelling candidacy that makes for a corrupt elected government. But one could assume other mechanisms. For example, it could be assumed, quite reasonably, that it is the experience itself of being a candidate in an electoral system that would corrupt almost anyone. It also could be, like you suggested before, that corruption is somehow directly correlated with the perception of competence (e.g., the ability to manipulate others is useful to having good public relations). Fourthly, it could be that the knowledge that one has a good chance of becoming a decision maker is corrupting in and of itself, as one comes to see this convenient fact as reflecting moral superiority.

    I think all those mechanisms have at least some degree of plausibility. More mechanisms (and probably shades of the mechanisms above) can be developed. (Come to think of it – developing a taxonomic model of mechanisms of corruption would probably be an interesting exercise.) The post argues that randomization is a way to counter any such corruption mechanism and any combination of such mechanisms.

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  16. OK, that helps. But then it seems to me that your model depends upon the assumption that 1) the corrupting influence can tell in advance which candidates are corruptible and which are not (otherwise, even if it could influence elections, it could do nothing to put corruptible people in there), and 2) the ordinary voter cannot tell in advance which candidates are corruptible (otherwise, nominating them would do no good–any non-corruptible candidate would automatically win). Is that right?

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  17. Peter,

    I take it you are referring to the first scenario I describe above:

    > I assumed that there is some innate property of “corruptibility” that afflicts 10% of the population. I also assumed that this innate property is not a-priori correlated with any other attribute (e.g., competence or perception of competence). In this scenario, it is the selection process of the corruptible among those with the potential for a compelling candidacy that makes for a corrupt elected government.

    I am happy to analyze this scenario, but I’d like to emphasize again that it is just one possible (and very abstract) scenario. The plausibility of this particular scenario does not bear directly on the usefulness of the basic model of corruption as an adversarial agent.

    > it seems to me that your model depends upon the assumption that 1) the corrupting influence can tell in advance which candidates are corruptible and which are not (otherwise, even if it could influence elections, it could do nothing to put corruptible people in there),

    Yes – the corrupting agent can test the candidate-worthy person thoroughly and on an ongoing basis as the person is being gradually promoted from the status of a mostly anonymous individual to the rank of a political officer wielding significant power. The corrupting agent can assign very specific tasks to the candidate and decide whether they were carried out satisfactorily. Like an employer who can select whom to promote from a field of many applicants, the corrupting agent can select the best performing aspirant based on a long and detailed track record. Of course, occasionally, the corrupting process may fail and a candidate that is considered by the agent to be reliably corrupt refuses, once in power, to follow directions. FDR comes to mind as a possible example.

    > and 2) the ordinary voter cannot tell in advance which candidates are corruptible (otherwise, nominating them would do no good–any non-corruptible candidate would automatically win).

    First, it is clear that the average voter does have much less information about a candidate than the candidate’s handlers and financial backers. Most voters learn about candidates only in the last few months before elections. All they do learn is what is transmitted to them through mass media, in the form of either “news” or campaign ads – and either way manipulated by interested parties. They may hear that a certain candidate served some special interests, but tracking down the details is difficult, and in any case would provide information about only one anecdote which may or may not reflect the true record of the candidate. Spending the effort required to ascertain the true nature of the candidate makes no sense when considering the minuscule impact that a single vote has on the outcome of an election. Thus, even if a voter has in theory the ability to discover who a candidate really is, it is unlikely that they would spend the huge effort of doing so.

    However, the assumption of lack of information – as plausible as it is – is not necessary to explain the success of corrupt candidates: If the corrupting agent has done her job well, any candidate that has enough resources to be known to more than a small percentage – say, p% – of the population would be corrupt. Thus, any non-corrupt candidate can, at most, win p% of the vote. Therefore, even if we assume that almost everybody is able to identify the corrupt candidates, it is enough for the corrupt candidates to either serve or fool a slightly larger proportion of the population than p% in order to overcome any non-corrupt candidate.

    Furthermore, knowing that minor candidates have very little chance of winning, people might decide that voting for a lesser-evil well-known corrupt candidate would serve their interests better than voting for a non-corrupt, nearly anonymous candidate. Thus, people might very well choose to vote for candidates they know are in the service of antagonistic forces simply because they think that by doing so they reduce the chance of having an even worse corrupt candidate win.

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  18. I’m just pushing on your assumptions to make sure they’ll do the work you want them to do. (As you know, I do likes me a little game theory now and again…) My concern here is that in your model, voters might reasonably anticipate that the candidates they know best are corrupt. It’s kinda like the old line from Thomas Moore–anyone who wants to run for office is automatically disqualified. If the only difference between candidates is their corruptibility, and if the candidate selection process produces disproportionately many corrupt candidates, then I should literally prefer to vote for any random person off the street over any of the mainstream candidates. Who cares if they’re unknown, or have no chance of winning? All the major candidates are likely to be corrupt, and therefore all equally suck. Such would seem to be the logic of the argument.

    I think you’re adding some other factor, like competence or ideological similarity, to explain why people might vote for candidates likely to be corrupt/corruptible. Without such an assumption, either voters cannot understand how the process works, or they’re simply stupid. And one of the cardinal assumptions in game theory is that all players play their best response given the information available to them.

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  19. > I’m just pushing on your assumptions to make sure they’ll do the work you want them to do.

    My pleasure – really. I am only noting that when we are discussing a particular set of assumptions within the space of possible assumptions that are consistent with basic model I suggested, then any conclusions that we arrive at may be a feature of those particular assumptions rather than of the basic model.

    > My concern here is that in your model, voters might reasonably anticipate that the candidates they know best are corrupt. It’s kinda like the old line from Thomas Moore–anyone who wants to run for office is automatically disqualified.

    The idea that any person that is widely known is under suspicion of being corrupt is indeed a basic feature of the model. In my treatment I assume that this idea is part of the conventional wisdom. How widely this idea is accepted in the reality is an interesting question.

    As the aphorism you quoted suggests, there does tend to a general suspicion of people who aspire to office. (By the way, I was not able to track down a source – do you have any?) The problem for a fundamental reform is that reformers tend to ascribe the corruption of candidates to various superficial features of the electoral system (“money in politics” is prominent these days in the US, for example, but in the past other supposed root causes were offered, and reforms such as the secret ballot were implemented in response). If it is recognized that corruption is inherent in the “principle of distinction”, so that no amount of tweaking of the electoral system can eliminate it, fundamental reform would be that much closer.

    > If the only difference between candidates is their corruptibility, […]

    You seem to imply that anyone who suspects that all the major candidates are corrupt would never vote for them, but this is simply not true – as my own personal experience tells me.

    There could easily be differences between corrupt candidates. Some are more corrupt than others, some are corrupt but in ways that are suitable to my interests to some extent, some are more competent than others, etc. Thus, a lesser-evil strategy is completely rational – it is the product of neither delusion nor stupidity. And, indeed, the lesser-evil argument is a major feature of real-life campaigns.

    Furthermore, it is exactly the argument of minor candidates that the differences between the major candidates are so little as to rule out the use of a lesser-evil strategy (Nader’s Tweedledum-and-Tweedledee line).

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  20. […] and lower the quality of government. Such an understanding is useful as background to evaluating the potential of sortition in reducing corruption. GA_googleAddAttr("AdOpt", "1"); GA_googleAddAttr("Origin", "other"); […]

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  21. […] A fairly interesting discussion of sortition can be found here. The top post makes an argument for sortition which is based on the idea of using randomness to deny an opponent a winning strategy. I pursued a similar line of thought here. […]

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