PUBLIC GOODS, EXTERNALITIES, AND THE COMMONS

PUBLIC GOODS, EXTERNALITIES, AND THE COMMONS

Chapter 10 of Analyzing Politics  

K.A. Shepsle

 A Summary 

Public Goods and Politics

• Public goods are nonexcludable (anyone can enjoy them whether they have paid or not), and nonrival (the use by one person does not diminish the availability of the good for se by someone else). The classic example is the lighthouse.
• Because anyone can enjoy it, producers of public goods are reluctant to provide them as they cannot extract a payment for so supplying. Thus the amount supplied will probably be a lot less than the optimum based on what people would pay if they had to.
• If the producer can be granted some sort of monopoly right then he will provide the good. E.g. if the lighthouse shows ships to harbour, and the owner of the harbour owns the lighthouse then he can charge extra for the harbour facilities and that way make a profit on the lighthouse. This only works if there are no competing harbours that could provide the services at lower cost free riding on the lighthouse owner’s provision of the lighthouse. Thus political protection of monopoly rights are important.
• Individuals meanwhile are incentivized to use the goods without paying for them. Potential producers understand this and thus will not produce unless they can find some means to elicit contributions.

 Public Supply

• Public goods then may be undersupplied relative to what society demands. An alternative is to let the government provide them as it can compel contributions through taxes. This is not as neat a solution as it may first seem, as public good provision by government is generally the fruit of some collective action that encourages the government to provide that particular good. So if the public good benefit is distributed widely and irrespective of whether an individual contributed to arguing for it, then free-riding will occur, and collective action will be hampered. Various select incentives etc. could be offered.
• These collective action problems are problems relating to consumption. Here large groups of consumers of public goods are unable to organize to argue for them. However, public goods are not just consumed, they are supplied. The government does not literally make the concrete used to build a network of roads; the work is subcontracted out. These subcontracted groups benefit greatly from providing the public goods to the government, and as they are smaller privileged groups they will not be subject to the same type of collective action problems as the consumers. Thus various interest groups that represent producers are likely to argue for public good provision.
• Yet government provision is not a simple option. Whilst legislators may generally approve of producing public goods they may be more concerned with getting $s to their constituents to improve reelection chances. Thus public good provision may be less efficient due to these distracting factors. Additionally, many public goods works take a long time to materialize, much longer than the time horizon of the regular politician. This can incentivize them toward flashy short term projects rather than long term successful provision. The drive to privatize has occurred partly in the hope that the private sector incentives will be better aligned to social objectives than under the former direct public provision.

 The Commons

• If each villager is contemplating adding a head of cattle to graze on a common piece of land he does not take into account the cost of doing so. If the common is large and the village small this will not be a problem. But if demands on the common grow and now villager has an incentive to restrict his use, the land will be overgrazed and ultimately destroyed. This is what Hardin called “the tragedy of the commons”.
• This is a problem of private and social incentives. Socially everyone knows that if they all graze an extra head of cattle they will all lose, but privately everyone knows that if they add just one more head there will be a negligible difference, they themselves will be better off, and no one will suffer. But as everyone faces this prisoner’s type dilemma, the result is overgrazing.
• The problems relate to imperfect property rights. If everyone owned well defined plots, or someone owned the whole common there would be the incentives associated with private ownership of a private good, and this means preserving the value of the asset. An individual would not overgraze his own land in the absence of strange circumstances.
• Ostrom outlines ways of dealing with the commons problem without reverting to private ownership. These are mechanisms that have clearly defined boundaries, a congruence of rules, monitoring arrangements, graduated punishments for defectors, and low cost means of resolving disputes. In other words managing a commons is a political problem – cooperation is required for preservation, and thus some form of political agreement regarding self-restraint is needed to prevent tragedy.

 

COLLECTIVE ACTION

COLLECTIVE ACTION

Chapter 9 of Analyzing Politics  

K.A. Shepsle

 A Summary

Multiperson Cooperation

• Groups consist of individuals who bear some cost or make some contribution in pursuit of a common goal. In the simplest form persons may either contribute or not contribute to the group enterprise. If the number of contributors is sufficiently large the goal is attained, if not, then the objective is not met. However, if the goal is attained, each member of the group benefits irrespective of whether or not they have contributed.
• It is important to know what level of contribution is needed for attaining the goal.
• In the case of unanimous contribution full participation is needed. There is a cost, C, and a benefit B from attaining the goal. If C>B then no one will contribute no matter how many other people might. If B>C then one of two things is possible:

1. No one contributes. This is an equilibrium because if no one contributes the jth person would not reconsider her choice, as the payoff would only be –C. The choice between not contribute (getting 0) or contribute (getting –C) always come out in favour of not contribute.
2. Everyone contributes. This is also equilibrium as the jth person would not reconsider contributing as the options are every contributes (getting B-C>0), or everyone except me contributes (getting 0).

• Thus it is possible to be stuck in an equilibrium trap in which no one contributes even though all would be better off contributing. However, because everyone’s participation is essential and everyone knows this and knows everyone else knows it, it is likely that everyone contributing will be the outcome.
• In the case of non-unanimous participation, of a group n at least k contributors are necessary. If fewer than k-1 of the group members are contributing, the jth person will not want to contribute as she will receive –C if she contributes when she would prefer just to receive 0 (by not contributing). In fact, only if exactly k-1 people are contributing is the jth’s persons contribution absolutely essential as the choices for her are not contribute (get 0) or contribute (getting B-C>0). This suggests there are two equilibrium outcomes:

1. No one contributes. The jth person will not reconsider as 0>-C (payoff from not contributing greater than contributing when goal is not achieved).
2. Exactly k people contribute. Those not contributing get B, and prefer this to contributing and getting B-C>0. Those contributing get B-C>0 which is better than any of them not contributing in which case they get 0. In other words exactly k individuals will have to believe their contribution is necessary, and that they and only they are likely to contribute.

• Which outcome pertains will depend upon a variety of factors. If n is large as k is large relative to n then people know that a lot of support is needed, and will tend to believe their contribution necessary. Thus k or probably >k will contribute. As k reduces in relative size this pressure will disappear. Cooperation in other words is harder to achieve when it seem obvious that each individual’s contributions is probably inessential.
• There may be some people who always prefer to do the right thing and contribute and thus if k gets really small the chances of success may again get better.
• As n gets large the psychological identification with the group probably affects the utiles enjoyed from achieving the joint goal, and this makes cooperation less likely, as benefit that greatly outweighs the cost will make participation more probable. This is the same as if the C gets large.

 Olson’s Collective Action

• Individuals are tempted to free ride on the efforts of others.
• This is especially so if the individual is not very significant in achieving the group goal (k is small relative to n).
• Olson claims that this temptation is an especial problem for large groups for three reasons:

1. Large groups tend to be anonymous. This makes it hard to forge a group identity around which there will be pressure to contribute.
2. Anonymity in the large group context means that the claim that no individual contribution is essential is more plausible. If lots of people contribute then the individual need not, if few people contribute then his efforts will make no difference.
3. Enforcement is harder in larger groups. The slacker cannot be prevented from enjoying the fruits of the collective action. In anonymous groups it will not even be possible to identify those that have contributed from those that have not.

• Small groups on the other hand are more personal and thus allow for interpersonal pressure. Individual contributions may make a real difference, and everyone knows who the slackers are. Punishment is thus easier to effect. Repeated play further enhances these features.
• The same logic of large versus small also applies within groups, when less powerful members may free ride on the contributions of the most powerful in order to achieve the goal e.g. NATO.

 Byproducts

• We see instances of large scale collective action. How are these explained?
• Groups achieve their goals by offering to individuals more than simply the benefits of achieving their goals. They receive these conditional on having contributed. So the motivational force for participation may in fact be these selective incentives, byproducts of the goal attainment. Groups that only provide the stated benefit will thus have a harder time organizing.

 Political Entrepreneurs

• One additional observation made by Wagner to the Olson theory is regarding the role of political entrepreneurs. Group action is often sustained by not only selective incentives, but by the efforts of specific individuals, leaders, etc. These individuals receive a different set of incentives which accrue to them pursuant to organizing and maintaining an otherwise latent group.
• In general this entrepreneur sees a prospective cooperation dividend, and for a price (votes, power etc.), or for a percentage of the dividend, the individual will bear the costs of organization, monitoring slack behaviour, and administering selective incentives.
• Thus the idea of an institutional solution to collective action problems is introduced.
• NB, some people may contribute irrespective of incentives, punishment, as to contribute conforms to their ideology or belief system or because they want to be a part of a social movement.

 Voting and Collective Action

• A person has a preferred candidate out of a two horse race. She will receive a benefit B if he is elected. She incurs a cost –C which she must bear in order to vote (going to the polls, information gathering etc.). Again B-C > 0. This is a very simple application of the above logic. If more than 50% of the electorate vote for her candidate she receives B irrespective of whether she votes. As B is better than B-C she will not vote. If more than 50% of the population vote for the other candidate she can either receive 0-C or just 0 (voting and non-voting), so she will always choose to not vote. If both receive exactly 50% then she can break the tie in her favour. Assuming that if a tie occurs there is a coin toss to decide the outcome she now faces payoffs of 0.5B (expected value of lottery), or B. As B is better she will vote. If the other candidate gets 50%+1 vote she can vote and institute a tie meaning the lottery will be entered into. Thus she receives expected benefit of 0.5B rather than the no vote payoff of 0.
• So only if there is a dead heat, or a loss of 1 single vote is it rational for her to vote in the election. The likelihood of there being a tie in the US election is infinitesimally small so it is very unlikely that a sensible person will conclude that they should vote. This is the case even when voting is very inexpensive for the voter.
• When seeking to explain the prevalence of people voting Riker and Ordeshook claim there are experiential as well as instrumental benefits from voting – warm glow etc.

 

 

VOTING METHODS AND ELECTORAL SYSTEMS

VOTING METHODS AND ELECTORAL SYSTEMS

Chapter 7 of Analyzing Politics  

K.A. Shepsle

A Summary 

Voting Methods

• Which voting method is chosen will affect the outcome given heterogeneous preference ordering.
• Examples of types of voting system:
  • Simple plurality: Each voter casts a vote for a single alternative and the alternative with most votes wins.
  • Plurality runoff – single vote, single alternative, and two alternatives with most votes move to next round in which balloting is repeated.
  • Sequential runoff: single vote, single alternative, then alternative with fewest votes eliminated and process repeated until there is one alternative left.
  • Condorcet Procedure – pairwise round robin tournament.
  • There are many more.
  • Given static preference ordering over a set of alternatives each method is capable of producing a totally different outcome. Thus the rules for preference aggregation matter a lot.
  • May need to think about the costs to voters in terms of how demanding a system is, and how much information they will need to gather in order to vote.
  • Also, the system chosen may not only change outcomes, but change the alternatives, as which candidates, policies are proposed will depend upon their ability to triumph. Candidates are endogenous to the voting system.
  • How then do we talk about the will of the group when using different methods reveals different group preference results?

 Electoral Systems

• The voting method in elections will depend upon whether the core value of the system in question is governance or representation. The former is associated with plurality means of voting – political representatives are able to act decisively and govern. The latter is associated with proportional representation whereby those elected represent the beliefs and preferences of the electorate. Generally plurality voting is for candidates, and PR voting is for parties.

 Plurality: First past the Post

• Each voter gets one vote and the candidate with most votes (not necessarily a majority) wins. If the constituency only gets one member they will not be very representative of the electorate assuming they are diverse bunch. If district magnitude is larger than the system will be more representative of the heterogeneity of the electorate, but it also means a bigger legislature and this can be harder to govern and ultimate take action on public policy which is surely the job of government.
• There are different types of plurality voting:
  • Single non-transferable vote: one vote, but the k highest vote getters are elected, when k is set beforehand.
  • Limited vote: more than one vote, but still allowing for k winners
  • Cumulative vote: voters may cumulate their votes for candidates e.g. cast both for 1^st preference. This encourages minority representation as well-organized minority candidates can win seats.
  • The equilibrium tendency of plurality systems depends upon the number of possible candidates in a district. Forces will either be centripetal (candidates converge to median), or centrifugal (candidates distribute along the spectrum).
  • Cox shows that when cumulation is not allowed, if the number of candidates is small enough relative to the number of votes that can be cast per voter then centripetal forces will dominate. But if the number of candidates is large then centrifugal forces operate to disperse the candidates along the continuum in equilibrium. When cumulation is allowed, the centrifugal forces always operate. E.g. Japan where there are 3-5 candidates per district, but only one vote allowed, there is no observed clustering on the median voter.

 Plurality: Single Transferable Vote

• Each voter reports his entire preference ordering. One a candidate reaches a quota of voters he gains a seat and the second preferences indicated on his ballot papers are distributed to the relevant other candidates. In this way another candidate may reach the quota and the process is repeated until the number of candidates to be admitted is reached. If upon transfer no other candidate has enough votes to make the quota, the candidate with the least first place votes is eliminated and his second preferences are distributed.
• This system means that a candidate has to energize his own supporters and to get listed high up the preferences of those supporting other candidates to get their reassigned votes.

 Proportional Representation

• The aim is produce a legislature that mirrors the preferences of the whole society. A PR system tends to reproduce the main social cleavages.
• Systems differ primarily in how they deal with fractional seats (a candidate get 4.35% of vote but can’t have 4.45 seats), and what the specified minimum is in order to get at least one seat (in Poland this is 1/450^th of the vote, in Germany it is 5% – high thresholds make the system more disproportional).
• Duverger’s Law suggests that FPTP with single member districts are strongly associated with two party/candidate competition. Third parties will not enter as they rarely have a chance of winning as voters will not waste votes on candidates that cannot win, even if they best represent their preferences. This is supported empirically. The second part of the law states that PR systems are associated with multiparty systems. Whilst this is supported empirically the analytical link is not well understood.

 Conclusion

• FPTP systems resolve conflicts before the legislative process begins. This allows the winning party, who will often command a majority, to govern in the manner in which they see fit, constrained by their campaign promises and the need to win the following election etc.
• PR systems defer this conflict until the legislative process begins. They reflect rather than resolve political conflict, and the legislative process is a means of discovering the manner of resolution.

SPATIAL MODELS OF MAJORITY RULE

SPATIAL MODELS OF MAJORITY RULE

Chapter 5 of Analyzing Politics  

K.A. Shepsle

A Summary 

Spatial Formulation

• If preferences order themselves in particular ways that reflect a sort of consensus then group decisions by majority rule can occur. When preferences are mapped on a graph with utility on the y axis and a scale of what is being decided on the x axis (e.g. a left wing right wing scale), and each individual has a most preferred point and preferences that decline as points further away in each direction are taken up, then preferences are said to be single peaked.

 

• The above graph shows single peaked preferences.
• So if a policy scale of Left to Right is used, an individual i has a most preferred policy x*. This is the bliss point the most preferred point on the scale, the point where he gets the maximum utility. As the policy moves away from x* in either direction his utility decreases. So if the policy is at a point x which is away from his preferred point, we can describe a set of alternatives (winset) which he would strictly prefer to x and naturally this set will include the point x*. If x>x* then he prefers all polices x-x* and also all policies x*-(x-x*) i.e. the set is symmetrical around his preferred point x*. This is the case for all individuals, and the sets will overlap to a certain degree meaning there are policy points in common that certain individuals prefer to the point x.
• We need to know which set of points a majority prefers to x. This is the majority win set. If there is some alternative to x, say Y that has an empty winset (written W(Y) = ∅) then there is no possible coalition that any majority of choosers prefers to this point. This would be a good candidate for the group choice. If the winset is not empty, then there is a point preferred to Y that a majority prefers so it would be hard to argue that the group choice should be Y.
• However, we know because of Arrow that it is possible for majority preferences to cycle meaning there is no point at which the winset is empty. But, if preferences are restricted by being single peaked it is easy to show that the ideal point of the median voter has an empty winset.
• Imagine a group of 5 legislators with single peaked preferences, as in the above graph. If policy is at any point that to the right of the 3 legislator’s bliss point, then a majority of legislators 1,2,3 will prefer the bliss point of the legislator 3 to that policy. For any policy to the right of the bliss point of legislator 3, then a coalition of 3,4,5 will prefer the bliss point of legislator 3 to that policy. However, when the policy is at the bliss of legislator 3 exactly, 4 and 5 may prefer points to the right, and 1 and 2 may prefer points the left, but no majority will prefer any point to either the left or the right. Hence the x*  of legislator 3 has an empty winset and is the majority choice.
• The assumptions behind this are that there are an odd number of legislators (otherwise the preferred point will be midway between the bliss points of the middle two legislators), that everyone participates in the vote, and that those voting do so sincerely.

 Multidimensional

• Things become more complex when more than one dimension is being decided upon. See the chapter for a clear discussion.
• The upshot is that in a case with 3 legislators deciding upon 2 issues simultaneously, if legislators 1 and 2’s bliss points are distributed symmetrically around the bliss point of the median legislator, then the majority choice is legislator 2’s bliss point.
• With more legislators, Plott’s theorem states that if the ideal points are distributed in a radically symmetrical fashion then the winset of the preferred point of the median legislator has an empty winset. This describes the centripetal tendency observed in the one dimensional setting studied by Black.
• However, this result is highly sensitive to movements in the ideal points of the legislators. In reality it would be very odd if ideal points were distributed radically symmetrically around that of the median.
• Indeed McKelvey’s Chaos Theorem shows that in the absence of such a symmetrical distribution there is no empty winset point Instead there is chaos, no Condorcet winner, and anything can happen with the result that the final outcome can be determined by whoever controls the order of voting. As some point is always preferred by a majority it is difficult to justify any particular group choice.

 Spatial Elections

• Political competition is a contest between those seeking to be in power. They appeal to voters using different policy platforms. For Antony Downs this meant that politicians seek to maximize votes.
• Politicians are represented at some point on the left-right scale. Each voter has single peaked preferences and a preferred point on this ideological scale. Each voter chooses the politician closest to their ideal point.
• If a leftist candidate is positioned somewhere to the left of the median voter and a right wing candidate is deciding what platform to offer, in order to maximize votes he should go a tiny way to the right of the Leftist candidate, and since L is already to the left of the midpoint of voter distribution R will get more than half the votes and win the election.
• L’s location divides the electorate in 2, those with ideals further right, and those with ideals further left. R must then position himself just next to L on the side of the larger group. L knows he will then get the smaller group, so in order to maximize his votes he needs to make that smaller group as large as possible. She does this by selecting ideal point of the median voter. R does the same and they now win the election with 50% probability each.
• If they announce their platforms simultaneously (rather than sequentially as above), the only point on the scale that is not vulnerable is the ideal point of the median voter.
• Perhaps they can change their platforms once in office. If the both announce policies on the same side of the median, there will be leapfrogging toward the median voter. If the announce on opposite sides they will both home in on the median from each side. In either case there is convergence toward the ideal point of the median voter.
• If both L and R are at the median, a third party could snuggle up close on one side and claim close to 50% of the vote, leaving L and R to share the remaining 50%. If L and R are sufficiently widely dispersed then she can enter in between and win all votes between her position and midway to the L position, and midway to the R position. If this part of the electorate is sufficient, she will win the election.
• There must in that case be entry-deterrence  locations for L and R such that a third party does not enter the race and win. Thus, there are conditions where parties do not converge upon the median.
• Other instances will occur when politicians have their own preferences which are known to the electorate. In this case they may run on policy of the median voter but voters will not believe them. They will suspect that once in office the politician will  implement his preferred policies. Voters will vote on which politician’s true preferences are closer to their ideal point. The politician is unable to credibly commit. Thus there will not be convergence.
• Even supposing that candidates can make credible promises and that they care deeply about what policies are implemented, they will still have incentive to converge on the median. If the position of L and R are equidistant from the median, then they have a 50/50 chance of winning. But, L could move just a tiny shade inwards at little cost to her and win the election outright. But R has now lost the election, and L’s policies are very costly for him. He could avoid this outcome if he too moved just a shade toward the centre. And so on, until the median is reached.
• We do indeed observe that leaders try to tone down their extremist policies in order to win elections.
• Convergence is not always complete. Politicians may fear alienating their base supporters and being punish in the polls, or they fear a new entrant.

 Spatial Legislatures

• As above it is the position of the median legislator that is important for policy decisions. If changes to the status quo can be offered and voted upon repeatedly, policy will converge upon his ideal point.

Things change if there is committee system in place. There are three possible decision making regimes:

1. Pure majority rule – there is a status quo and any legislator can offer a motion to change it
2. Closed-rule committee system – committee decides whether to propose a motion to change status quo and the legislature can either accept or reject the proposal but they cannot amend it.
3. Open-rule committee system – committee decides whether to offer motion and the legislature can amend the proposal.

Pure majority rule: policy converges on the median policy and it will not move from there. This is the case no matter what the status quo is. All we need to know is the SQ and M_L point.

Closed rule committee system: the M_C (median committee member) point is also relevant. The set of points around the median legislator bounded by the SQ and its reflection on the opposite side of the median legislator is the opportunity set for the committee. They can propose policies within this set and get a yes vote. If outside this set they get a no vote, and hence will not propose any motion. There are three cases:

1. SQ<M_L<M_C: In this case x* is the right bound of the preferred to SQ set of the median legislator. If M_C<x* then the committee proposes its preferred point and gets a yes vote as its ideal point is within the set that will be approved by legislative majority. If M_C>x* then the best the committee can do is to propose x* which will move the policy closer to its ideal point. It cannot propose anything closer to its ideal point and get a yes vote in the legislature.
2. SQ<M_C<M_L: In this case the ideal committee point is within the preferred to SQ set of the legislature, so the committee can propose its preferred point and get a yes vote in the legislature.
3. M_L<SQ<M_C: The committee and the house want to move in opposite directions. Thus the committee keeps the gates closed as it would be impossible to get a yes vote for any policy closer to its ideal point.

• The upshot of this is that agenda power can prevent centripetal forces applying as outcomes are tugged in the direction of the agenda setting group.

Open Rule committee system: When the gates remain closed, the SQ prevails. If the gates are opened the M_L point is reached by amendments from the house. Nothing else is possible. Thus if the M_C prefers M_L to SQ then it will make a motion, if not it will keep the gates closed.

• If policy space is multidimensional and the ideal points are not distributed symmetrically around the median then the Chaos Theorem holds. However, if an agenda setter has the power to sequence the decisions, the outcome is the multidimensional median. The median ideal point on each dimension prevails.

 

GROUP CHOICE ANALYSIS

GROUP CHOICE ANALYSIS

Chapters 3-4 of Analyzing Politics  

K.A. Shepsle

A Summary 

Getting Started

• If a group has to decide between a set of feasible actions one way to proceed is by unanimous agreement. However, preferences may be ordered such that a solution is not possible, tastes are too heterogeneous. E.g. A, B and C to decide between x, y and z. A: x>y>z B: y>z>x C: z>y>x. The group does not unanimously share the first preference. Likewise majority rule fails to provide an answer as no two members share the same first preference. A round robin tournament where each outcome plays each outcome and if one is preferred by a majority to all the other it is the group choice is also possible. x vs. y yields y; and x vs. z yields z; and z vs. y yields y. Thus y is the majority preference of the group. But as different majorities prefer y to each other alternative there is incentive not to vote sincerely, that is to be strategic. For example player C could lie in the first round and vote for x. In that way the outcome would be x, z, y, i.e. the tournament would have no winner. So this method only works if people vote sincerely.
• The preferences may be ordered such that in a round robin tournament there is a cycle of preferences. That is whilst every individual has transitive preferences, when they are aggregated the group preferences are ordered x>y>z>x. This is a preference cycle, and would occur in the above example if player C: z>x>y. To solve this problem an agenda is needed whereby one player decides upon the ordering of the voting in a system where the first pair is voted on, and the winning item then plays the last item, and the winner of that is the group choice. Any of the players can get their most preferred outcome if they believe the others will vote sincerely.

 Condorcet Cycles

• Even though individuals have consistent preferences the group may not. As the number of alternatives and the number of voters increases the probability of experiencing a majoritarian cycle approaches 1. This probability is radically smaller in small groups/few alternatives situations. In general though it means we cannot rely on majority rule to produce a coherent sense of what the group wants especially if there are no institutional mechanisms for keeping participation low or the number of alternatives small.
• In reality we do not always observe such cycles. This is because even though probability approaches 1, the cycle is dependent upon each possible ordering of preferences to be equally likely. However, normally what we observe is some interdependence among individuals, whereby people share the same preferences.
• e.g. if three mayors {A,B,C} have to divide an amount of money, there is no possible distribution of the funds that is not preferred by a majority to every other distribution. If they all start with a distribution {33.3%, 33.3%, 33.3%} a majority of A and B prefer {500, 500, 0}, but then a majority of A and C prefer {600, 0, 400}, and a majority of B and C prefer {0, 500, 500} and so on ad infinitum. The final outcome in the scenario will depend upon institutional features i.e. who has agenda power and how can they use it.
• Thus the only way to avoid preference cycles is to impose some sort of antimajoritarian restriction.

 Arrow’s Theorem

• The Condorcet paradox is a problem for any reasonable method of aggregating group preferences.
• The impossibility result follows: there exists no mechanism for translating individual preferences into coherent group preferences without some kind of dictatorial power. In other words preference aggregation and choice is either incoherent or dictatorial. There is a tradeoff thus between social rationality and the concentration of power. Concentrated power allows for social coherence as the dictator knows his own mind. So systems without such power may seem fairer, but they are also more likely to be inconsistent in ordering alternatives under consideration.
• This does not mean choices will always be inconsistent, only that it is impossible to rule out such choices. This means it may be possible for clever manipulative people to be strategic in exploiting this fact.
• The bottom line is that individuals may be rational, but the group need not be. This makes is difficult to speak of legislative intent when thinking about interpreting the law for example.

 Solutions

• Duncan Black thought that minimal forms of consensus other than unanimity could be sufficient to allow for coherent group choice.
• In particular if preferences are single peaked then majority rule works perfectly well despite legislators holding wildly divergent views on what the group ought to do.
• This will be evaluated further in chapter 5.

RATIONALITY: THE MODEL OF CHOICE

RATIONALITY: THE MODEL OF CHOICE

Chapters 2 of Analyzing Politics  

K.A. Shepsle

A Summary 

Rationality

• Individuals have preferences and they are self-interested in that they act in accordance with them. They operate in an uncertain external environment which affects the way they express their preferences. This means that often individuals do not have an exact sense of how an instrument or behavior relates to the outcome they desire. It is an individual’s beliefs that connect the instruments to the outcomes. Thus to be rational is to act in accordance with one’s preferences, and one’s beliefs. Individuals combine their beliefs about the external environment and their preferences for outcomes in that environment in a consistent manner.
• The individual is the basic unit of analysis.
• It is not important what motivates an individual’s preferences. All that matters is that the choices made are coherent in that they bear a logical relationship to his preferences.
• A choice is rational if the object chosen is at least as good as any other available according to the chooser’s preferences.

 Preferences

• Complete: alternatives are comparable. For any two possible alternatives the chooser either prefers one or is indifferent between them.
• Transitive: if x<y<z then x<z
• If these two conditions hold, the chooser has a preference ordering. Preferences that permit rational choices are in effect ordering principles.
• There may be inconsistencies in preferences particularly when the stakes are low and uncertainty is high i.e. the result has little consequence for the chooser. Behaviour will under these conditions be more random than rational.

 Maximization

• Preference ordering means an individual can take a set of objects and place them in an order that reflects personal tastes. Rationality is associated with being to so order, and also from being able to choose from as high up the order as is possible given the external environment. This last aspect is evidence of maximizing behaviour.

 Uncertainty

• Individuals cannot often choose the outcome directly; they must choose an instrument to obtain the outcome. A belief is a probability statement about the instruments effectiveness in obtaining the outcome desired. If a chooser knows what will occur he is operating under conditions of certainty. If he is not totally sure an instrument will lead to a particular outcome he is operating under conditions of risk. If the relationship between instrument and outcome is so imprecise that it is impossible to assign probabilities then he operates under conditions of uncertainty.
• In the last two cases, in order to see which course of action is best we assign utility numbers to outcomes which reflect the relative value of each. By assigning probabilities and calculating expected utilities we can choose the best lottery by choosing the lottery with the highest expected utility. Rationality demands that the individual choose the action that maximizes expected utility.