Abstract
I develop a hybrid of direct democracy and representative democracy in which each citizen may vote directly on each issue, or delegate his vote on any issue to a representative (that is, a proxy) of his own choosing. I construct both an axiomatic argument for such a system and an argument based on its ability to ameliorate the information problems inherent in both direct and representative democracy. I also propose practical measures for implementation, including new variations on existing proxy system proposals. These new variations include a ‘Dodgsonesque’ procedure, a proportional agenda-setting procedure, a provision for virtual committees, and a provision for continual consideration of issues.
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Notes
If current systems of representative democracy were universally held in high esteem, this question might be of little more than academic interest. But in fact, dissatisfaction with these institutions is quite widespread even in established democracies. For example, America: Newport (2014) reports that only 14 % of survey respondents approve of the US Congress’s handling of its job (with an average of approximately 15 % since the beginning of 2011), and Riffkin (2014) reports that only 7 % of survey respondents have “a great deal” or “quite a lot” of confidence in the US Congress as an institution. Where approval of the current legislative system is this low, it is logical to give serious consideration to alternatives.
For a concise overview of arguments for and against proportional representation, see Reynolds et al. (2005).
As the authors note, this proposal has parallels in ancient Athenian democracy, where many offices were decided by lot. For example, Aristotle writes in book 4, part 9 of his Politics that “the appointment of magistrates by lot is thought to be democratic, and the election of them oligarchic”.
See Ottesen (2003).
See http://liquidfeedback.org and Behrens et al (2014).
See e.g. the entries for “pure democracy” in the Merriam-Webster and American Heritage dictionaries: http://www.merriam-webster.com and http://ahdictionary.com.
Although it might be tempting to reject this reasoning on the grounds that voters in an ideal democracy would be fully informed on every issue, this objection cannot be applied to the full range of public decisions made by modern governments, as this would surely place too great a burden on citizens’ time.
Black (1948) shows that the median position is an equilibrium in iterative majority rule if the issue space is one-dimensional and voters’ preferences are single peaked. Here, I allow for multi-dimensional issue space and make no explicit single-peakedness assumptions. Therefore, my assertion that the median vote is the outcome is more of an assumption than a result. That is, I assume for simplicity that voters are not strategic, that the voting process consists of voters indicating a value in each dimension, and that the election authority determines the outcomes by finding the median votes. Relaxing these assumptions (along with the independence assumption, thus allowing a voter’s preferences on one issue to depend on the outcome of another issue) would be an interesting challenge for anyone seeking to extend this model.
I share these goals with Alger’s (2006) analysis. My model differs in that it allows for multiple issue dimensions (which is useful when discussing the value of allowing voters to delegate to different representatives on different issues), and in that it includes the possibility that citizens vote with error (which is the most intuitive justification for representation of any sort).
See for example Green-Armytage (2014).
A related problem is disproportionality, i.e. the discrepancy between each party or group’s share of the vote and its share of the legislative voting power, caused by the requirement that each seat must possess equal voting weight.
See e.g. chapters 12–13 of Tideman (2006) for a discussion of these.
Caplan (2011) explores this idea in much more detail; he argues that voter errors will generally not cancel each other out, so that (using my terms) expressive loss will normally lead to systematic loss. Further, he correctly points out that democratic systems (like computers) are vulnerable to the “garbage in, garbage out” problem, but he doesn’t make distinctions among systems in terms of the expected quality of their output relative to the quality of their input. My emphasis here is different: whereas his purpose is to provide evidence that democracy is fundamentally flawed (which I grant, to some extent), my purpose is to improve the performance of democracy to the degree that is possible.
Or perhaps better still, multiple proxies; Sect. 5.6 explains how ‘virtual committees’ may be more effective than single proxies in this case.
In this framework, the precise condition is \( E_{i} \left[ {D_{ijm}^{2} } \right] - 2E_{i} \left[ {D_{ijm} \varepsilon_{jm} } \right] + E_{i} \left[ {\varepsilon_{jm}^{2} } \right] < E\left[ {\varepsilon_{im}^{2} } \right]. \)
This supposition is analogous to the idea of anti-paternalism, which is common in mainstream economic thought and which goes back at least to Mill (1859). If we suppose alternatively that some other authority can more effectively determine a voter’s best representative, how do we identify this authority? That is, it is possible for example that a wise an unselfish philosopher king may reach a better decision than a democratic majority, but we are still faced with the decision of how to choose this king, which brings us back to the same problem of aggregating individual opinions into a collective choice. Similarly, who can determine which voters are competent to decide this for themselves and which ones are not? Tests of intelligence or knowledge of current events are possible, but highly problematic, e.g. in that they depend once again on the authority that is empowered to write them. Perhaps there are further arguments in favor of political paternalism that should be considered, but I do not pursue them here.
To resolve Shubik’s concern, we can make this period long enough to permit ample discussion and reflection. The number of issues is a matter of political choice, which should depend on the costs and benefits of direct voting.
Since the number of candidates would likely be very large, citizens should not be required to rank all of them. For the same reason, computerized ballots would be preferable to paper ballots. Individuals should be able to use the ballots of model voters to determine their ranking of the candidates, as with other issues.
That is, it is consistent with the goal of giving voters maximum freedom to choose their representatives.
A logical and empirically well-established result; see e.g. Section 13.5 of Mueller (2003).
By default, each voter’s share of remuneration may be divided according to the number of times he used the model vote of each proxy, as a ‘nudge’ toward this practice (But since voters could find ways to subvert attempts to enforce it more strictly, voters might as well be allowed to deviate from this default allocation as they see fit).
In the case of an individual serving both as a legislator and a proxy, the same cap would bind the sum of the two salaries.
Behrens et al. (2014) recommend the beatpath rule—defined in Schulze (2003)—for use with their proposed direct/proxy voting system. However (like most voting rules), beatpath may be vulnerable to strategic manipulation in a substantial fraction of cases; see e.g. Green-Armytage (2011), which finds that Condorcet–Hare hybrid rules are less likely to be manipulable. For this reason I would give preference to the Dodgsonesque rule described here when strategic voting is a concern, or to a Condorcet–Hare hybrid rule if the possibility of multiple rounds of voting is considered undesirable.
Charles Dodgson is better known by his pen name, Lewis Carroll. The “proposed rules” that I refer to here should not be confused with what is now commonly known as “Dodgson’s method”; the latter is drawn from later sections of Dodgson (1876), and uses a single round of voting rather than providing for additional rounds in the case of a majority rule cycle.
This is a candidate who, according to ranked ballots, would defeat any other candidate in a one-on-one majority vote. See de Condorcet (1785).
Also known as the Smith set, due to Smith (1973). It is the smallest non-empty set of candidates such that every candidate inside the set is preferred by a majority to every candidate outside the set. When there is a Condorcet winner, it is the sole member of the Smith set.
The reason for this particular choice of elimination methods is that it creates similarity with Condorcet–Hare hybrid rules.
If there is a sincere Condorcet winner w with respect to the voters’ sincere preferences, and everyone votes sincerely except for a faction of people who prefer another candidate q to w, then w will certainly still be a member of the minimal dominant set. The existence of a cycle gives members of the majority who prefer the sincere winner an opportunity to examine the votes cast for signs of strategic manipulation, and if they find any, to adjust their votes so as to cancel it out and elect the sincere winner. It is not obvious that such investigation and reversal will always be successful, but at least there is an opportunity to attempt it, whereas if only a single balloting is taken and the result is binding, there is a greater probability that the strategic incursion will go unchecked.
For example, the amount of money spent on a particular project or agency, the marginal tax rate on a particular type of income, the number of days that should be served in prison for a particular crime, the legal drinking age, etc. Section 6.6 below discusses specific examples in more detail. Disaggregating the policy space into one-dimensional issues when possible should increase the stability of outcomes; see e.g. Enelow and Hinich (1983), and chapter 5 of Mueller (2003).
A core equilibrium is defined as a situation in which no group of voters can gain a mutual advantage by changing their votes. The logic of this result is similar to that of Black’s (1948) median voter theorem. In brief, if votes are sincere, voters with preferences either above or below the median will not be able to affect the outcome by exaggerating the distance between their vote and the median. (If the procedure chose the average of the two middle values instead of choosing one of them at random, this would not hold for cases without a unique median, e.g. with voter ideal points at 0, 4, 6, and 10.) The procedure escapes the negative result of the Gibbard (1973) and Satterthwaite (1975) theorem because it does not satisfy the universal domain criterion.
It would also be possible to reserve some time for proportional issue generation by direct voting: First, model voters would be able to propose a wide range of issues to be addressed, in addition to the agenda decided on by the legislature. Second, the public would vote using STV among these issues to decide which ones would be considered.
The maximum number of options should be set prior to this vote, but voters may be able to choose a smaller number through the use of a ‘null option’ on the ballot. The status quo should be considered as one of the options. Something on the order of five to ten options should be sufficient for most issues.
In this essay I use male pronouns for voters and female pronouns for representatives.
The citizen could choose among a variety of single-winner voting rules, including e.g. Borda, Hare, beatpath, etc. It would be possible, if desired, to assign different voting weights to different committee members.
See Mueller (2003, chapter 5) for a review of the literature on lack of equilibrium in iterative majority rule.
I propose the following debate format. Rather than having a limited time for each response, representatives have a limited time to speak in each discussion period. This way, the participants can have something approaching a normal conversation, asking and answering questions, making short statements of just a sentence or two, and following specific trains of thought to the end, rather than giving lengthy speeches that only partially respond to each other. Participants should be allowed to pause their clocks to consider their replies and to ask questions of neutral on-site fact checkers. The videos of these debates, when completed, should be made available for free online, with and without the pauses edited out. The version without the pauses would be attractive to viewers by virtue of combining well-thought-out discussion with a relatively fast pace.
For example, they may be paid to participate, or stripped of some remuneration if they don’t participate.
Failing the introduction of such computerized voting booths, the creation of a social networking web site that allowed people to discuss upcoming votes, aggregate the opinions of proxy networks, and print convenient how-to-vote cards, could begin to provide some of the same benefits, albeit in a more limited capacity.
Note that anonymous voting of this kind would preclude a system of continual consideration.
That is, the system described in Sect. 5, which provides an electronic venue in which anyone may cast a model vote, explain the reasons for that vote, and discuss it with peers. This may serve as the basis for conversations that extend into other media, such as face-to-face, phone, television, etc.
For example, this may help some individuals to obtain jobs, or some non-profit organizations to obtain grants.
I leave this discussion rather brief, but I consider it to be an excellent topic for future research, ideally in collaboration with those who have a strong background in the theory of deliberative democracy in the tradition of Habermas (1991), Bessette (1980), Elster (1998), etc. That is, I’ve made a preliminary argument that a voluntary delegation system (ideally coupled with a series of debates as described in Sect. 5.8) may have the capacity to serve as a platform for citizens to create a more active, intellectually vibrant public sphere, but I hope for much more discussion on this topic. The theory of deliberative democracy has been used to criticize direct democracy in the form of referenda for lacking sufficient in-person deliberation—see e.g. Leib (2006)—and to develop “deliberative opinion polls”—see e.g. Fishkin (1991)—which have some features in common with Mueller et al.’s (1972) proposal for representative democracy via random selection. I suggest that voluntary delegation systems would be an interesting alternative to add to this conversation.
Cox (1997) provides a useful survey of the literature on strategic political behavior from an interdisciplinary perspective. The Gibbard (1973) and Satterthwaite (1975) theorem demonstrates that any single-winner system that doesn’t appoint a dictator or impose restrictions on the voters’ orderings of candidates will provide incentives for strategic voting in some circumstances. Nitzan (1985) and Chamberlin (1985) provide interesting early efforts to understand the vulnerabilities of different single-winner voting rules to individual manipulation and to coalitional manipulation, respectively. Green-Armytage (2014) provides a more recent look at strategic voting and nomination in several single-winner rules.
STV is designed to reduce the frequency of incentives for this type of strategy, but it is still not completely strategy-free.
Given this, it is not surprising to observe frequent negative campaigns that focus on portraying the opponent as a great evil. This causes discourse among politicians to be polarized, which in turn may cause ordinary citizens to become politically polarized, which the Pew Research Center (2014) finds to be increasingly the case in the US.
Dutta et al. (2001) show that all reasonable ranked ballot single-winner election rules provide incentives for candidates to strategically exit races in some circumstances.
Barro (1973) is one of the first to describe the problems of government in this way.
Olson (1965) gives a seminal analysis of the role of interest groups in collective decision-making.
That is, governments don’t face quite the same kind of pressure as firms in perfectly competitive markets to produce the most valuable outputs with the least costly inputs, in part because governments are by their nature not perfectly competitive organizations, except in extreme cases such as the governments-as-clubs imagined by Tiebout (1956).
Of course, a direct/proxy voting system is not perfectly immune from corruption. Just as it is sometimes mutually beneficial for an interested party to buy a traditional representative’s vote with an explicit or implicit quid pro quo, it is not inconceivable that someone might offer a bribe to a model voter. Therefore (as in the case of traditional representation) it is in the public interest to outlaw such exchanges as broadly as possible, and to prosecute them aggressively.
I do not claim that this selection is exhaustive. The purpose of this paper is not to settle all doubts about direct/proxy voting systems, but rather to convince the reader that they are interesting and promising enough to be worthy of further analysis, discussion, and experimentation.
For example, how many issues will be handled, and how complex will they be? Will the voting be done in person or online? How literate and computer-literate are the voters? How many languages should be represented?
Whether it is feasible to develop a verifiable and secure online implementation of direct/proxy voting is an interesting question, but one that is beyond the scope of this paper. The implementation using polling stations described in Sect. 5.9 allows more familiar methods of verification, such as the printing of paper voting receipts.
Similarly, it would be straightforward to use a median value procedure to determine the legal drinking age.
If marijuana use creates a negative externality, a Pigovian tax may be justified. Or, whether justified or not, the majority may aim for the tax rate that maximizes public revenue. Economists should be able to generate estimates for either of these.
Similar consideration may be given to other pollutants in general and other greenhouse gases in particular, e.g. methane, etc.
If carbon policy is determined by wise technocrats rather than by direct voting, the resulting decision may be more coherent. However, we still face the question of how these technocrats will be chosen. If the general public is unwise and set on a particular policy, will they permit the appointment of wise technocrats who may be expected to settle on quite a different policy? Meanwhile, it is especially difficult to imagine a democratic mechanism that could perfectly handle the externalities associated with carbon gas. One particular problem is that many of the people who are affected have yet to be born, so it is unclear how to include them in the bargaining process. Another problem is that the externality is global in scope, so that the optimal solution may require an intractably complex international bargaining process. It may be possible to design direct voting agendas that consider complicated Pareto compensation schemes, reciprocal reduction arrangements, etc., but I leave this for future inquiry.
What rule for the election or appointment of judges would best assure that they will protect the rights of minorities? Are judges who are elected by majorities or appointed by others who are elected by majorities able to do this reliably when the majority wishes to tyrannize a minority? These questions are fascinating but beyond our current scope.
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Green-Armytage, J. Direct voting and proxy voting. Const Polit Econ 26, 190–220 (2015). https://doi.org/10.1007/s10602-014-9176-9
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DOI: https://doi.org/10.1007/s10602-014-9176-9
Keywords
- Proxy voting
- Direct democracy
- Participatory democracy
- Deliberative democracy
- Liquid democracy
- Proportional representation