Public choice theory has been defined as the application of economic analysis to the study of politics. In other words, its subject is political economy in the classic sense. But one has to hasten to qualify this statement and say that 'public choice' is not a subject in its own right but rather a way of studying a subject viz political economy. Alternatively, it can be defined as the economic study of non-market decision-making. It takes the tools of economics and applies them to political issues for analysis. 
By this definition, public choice is an interdisciplinary field of enquiry.
Public choice applies economists' methods to politics, and in particular, to two central problems: (a) the collective action problem and (b) the problem of aggregating preferences. These arise from the scarcity of resources. Given the fact of scarcity of resources, every society must arrive at a rational and reasonable way of allocating them. There are four ways of doing these: (i) altruism, (ii) anarchy, (iii) market, and (iv) government. Economists have traditionally studied the third, almost to the exclusion of the other three. Most of the economic techniques were first used to explain how markets work in allocating resources. Even in the most market- oriented society, there are two sorts of public good that only governments can supply: rules and compensation for market failure. A rule is a public good that only government can provide and rules are inherently scarce: if there is a law against pollution of water, there cannot be at the same time a law allowing it. If anybody benefits from it, everybody does. But public goods are a problem because by definition they are indivisible. Because of indivisibility it is difficult to make consumers pay for them. Because people cannot be excluded from enjoying clean air, some may be tempted to 'free ride'-- to get them without paying. The inherent features of public goods make them excellent subjects for public choice methods. The second main branch of public choice is concerned with analysing expressions such as 'the people's choice' that involves institutions like committees and elections under democracy and other forms of governments. A country may have many people but only one government and one public policy on any matter. On some matters there may be many alternative decisions reflecting individual choices. But governments have to get from many individual choices one particular choice, aggregating them. Public choice theory deals with the possibilities or impossibilities of aggregating individual preferences in to social or collective choice or government decisions.
Democracy has some system of elections through which the voters elect a parliament which in turn forms a government both of which take collective decisions with the help of bureaucrats. The voters can be looked at as if they are consumers, the politicians as entrepreneurs, the bureaucrats as managers of firms and so on. So, democracy is one system of decision-making, connecting voters (citizens) with decisions made by politicians and implemented by bureaucrats. Does it succeed in aggregating individual preferences into social or collective choice? Public choice theory studies this important question and tries to give answers. It offers two main findings. First, aggregation from individual to collective preferences may not be well defined. Second, individual motives for actions may not fit collective preferences for outcomes even when the latter are well defined. The first class of findings casts doubt on majoritarian democracy. The second class is thought to yield a consensual justification for the coercive power of state, provided it is democratic.
THE PIONEERS: The early works that laid the foundation to public choice study were offshoots of mathematics. When two French mathematicians, J.C de Borda (1781) and M.de Condorcet (1785) wrote theorems that dealt with collective decision making, they had little inkling that their works would credit them with being the forerunners of public choice theory in future. Condorcet was the first person to discover the problem of cycling, the possibility when using the simple majority rule that an alternative x can lose to y in a vote between the two, y can lose to another alternative z, but z will lose to x. The existence of such possibility raises the issue of how a community can decide among these three alternatives, when a cycle exists and what the normative justifications for any choice made will be. It is obvious, however, that no cycle exists, if some alternative, y, can defeat both x and z. The literature on public choice has commemorated Condorcet's contribution by naming such an alternative like 'y' a 'Conodorcet winner'.
Condorcet made further contributions to the inchoate body of knowledge that later came to be known as 'public choice' by formulating a theory which he called 'jury theorem'. Jury theorem provides both a justification for making collective decision with the simple majority rule and for the institution of democracy. The theorem rests on three assumptions : (1) The community faces a binary choice between x and y, with only one of the two choices being the right choice for the community; (2) Everyone in the community wants to make the right choice; and (3) The probability that a citizen votes for the right choice is greater than 0.5. The theorem states that the probability that the community makes the right choice when it uses the simple majority rule increases as the number of voters increases, approaching one in the limit (0 to 1).
If one accepts the above premises it becomes obvious that the jury theorem formulated by Condorcet provides a normative case for simple majority rule, as in a democracy. Condorcet described the collective decision as one (in the scale of 0 to 1) regarding determination of a verdict by the community on an issue from which the epithet 'jury' is derived. The assumption that everyone (jury) wants to make the right decision is beyond controversy. The argument that the theorem also provides a justification for democracy, however, is not obvious and therefore, controversial. If anything, it is subtle in its implications in this regard. Condorcet imagines that everyone in a community agrees to have a good government that provides goods and services and collects taxes in a manner that maximises welfare of all citizens. In this scheme, each citizen votes for the party (out of two) that he or she believes will deliver what the community desires viz best government. If each citizen has greater than 0.5 probability of picking the party that will form the best government, democracy chooses the best government in a large electorate with near certainty.
The second and third assumptions in Condorcet's theorem assume great importance when the theorem is used as a defence of democracy. Citizens share a common goal i.e having a best government. Each citizen has a greater than 0.5 provability of picking the party that will provide the best government. Condorcet believes citizens just don't take chances in exercising their right to vote but study the past record and the manifestos of parties before making up their minds.
The assumption that everyone agrees in what constitutes best government becomes controversial when the whole range of activities (decisions) of governments are taken into consideration. If citizens disagree on what the government should do, there will be no ' right choice' for all citizens. Knowing this, parties will compete not only on the basis of how good they will be at promoting the community's welfare but also how that welfare should be defined Finally, when the electorate is large, comprising many people, the assumption that voters are well- informed becomes questionable. Almost all studies on competition among political parties using various models assume that voters know where the parties stand on various issues. But they do not assume where the parties should be located in the spectrum of issues. Because of the ambiguities and uncertainties of the assumptions, some economists do not use Condorcet jury theorem while studying public choice but some find it useful.
Condorcet's pioneering work, however, raised many of the questions with which the modern public choice theory has been concerned with: (a) Do individuals share common interests? (b) Is democracy stable or not? (c) Are voters sufficiently informed, facilitating aggregation of their preferences? (d) What voting rules should be used to aggregate the preferences of individuals?
Borda, Condorcet's contemporary French mathematician, was critical of the use of simple majority to aggregate preferences, as suggested by Condorcet's jury theorem. Instead, he proposed a rule that came to bear his name. He proposed that there are a given set of possible outcomes to a collective decision; each voter will assign a one (1) to his most preferred choice ; a two (2) to his second most preferred choice and so on. The scores given are then added to reflect voter's choice. The Borda-count rule selects as the winner the alternative receiving the lowest score. With only two alternatives from which to choose, the Borda-count is equivalent to the simple majority rule. But unlike Cindorcet's jury theorem, it avoids cycling
Some scholars include John Stuart Mill's 'Consideration on Representative Government' (1861) in the early studies on public choice. Though a work on political science, the logical analysis in the book makes it a useful preface to the study of public choice. The same can be said about K. Wicksel's essay on 'Just Taxation'(1896). Though a work on public finance, the article delineates a normative role for state and offers a robust defence of the unanimity rule for aggregating individual preferences.
EARLY MODERNS: As a modern day discipline, public choice came into being with the publication of articles by Duncan Black (1948), James M Buchanan (1949) and Kenneth J. Arrow (1950) in the late '40s and early '50s. Joseph Schumpeter stakes a claim as a senior contributor to the study on public choice before this trio but it was the threesome who ushered in the modern and formal study in the esoteric field of public choice.
Duncan Black wrote two articles, the second one being an extension of the first. He gave an account of the history of ideas underlying his work on public choice. His analysis takes up the theme of 'cycling' first mooted by Condorcet under simple majority rule and provides a proof of the median voter theorem. This theorem has been the analytical foundation for much of the empirical work on public choice.
Buchanan published several important articles in late '50s, but it was his work, 'The Calculus of Consent' (1952), co-authored by Gordon Tullock that established him as a leading authority on public choice. The book contains many interesting discussions on aspects of simple majority rule. But his most important contribution has been the analysis of distinction between constitutional stage of collective decision-making in which voting rules and other practices of democracy are selected and their application to the actual work of making collective choices.
Buchanan has written about 'politics without romance' by which he has highlighted the fact that politicians act more out of self-interest than the desire to promote public interest. His main thesis is that self-interest and other non-economic forces determine government policy. Should the electoral interests of an incumbent party be advanced more effectively through policies that create instability than through policies that promote stability, the promotion of stability is unlikely to be pursued,' he wrote (The Political Economy of Public Disorder,2009).To press further on the idea of self-interest he wrote: To continue in office, an incumbent politician must secure more votes than his challenger. Policies are instruments that politicians have to assist them in maintaining their incumbency. It is reasonable to view politicians as designing policies so as to enhance their electoral support.' (ibid) He concludes saying: Macroeconomic theory has tended to look upon government as having the function of keeping stable what would otherwise be an unstable economy . Once it is realised that macroeconomic policy emerges from within a political process, it quickly becomes apparent that the politically rational conduct of public policy may actually amplify rather than dampen instability (business cycle).
While Buchanan accepts the possibility of decision-making in a polity like democratic government and is sceptical only about the honesty of motive of policymakers, Kenneth Arrow raises question about the very possibility of decision-making under a democratic dispensation. Echoing Condorcet's problem of cyclic majorities, Arrow's General Possibility Theorem (also known as Impossibility Theorem) observes that there is no general rule for aggregating individual preferences to a social or collective choice that can meet certain acceptable criteria. The criteria are: A rule must select one and only one alternative, given a set of individual preferences; a rule must not permit anyone's preference to be the social choice regardless of what anyone else prefers; from among two alternatives a rule must choose the alternative that is unanimously preferred; with respect to any two alternatives, a rule must select an outcome on the basis of the individual's preferences between those two alternatives ; a rule must satisfy these requirements for any possible array of preferences. Since there is no such rule, political questions cannot be solved by majority rule and no society can be fully democratic.
It has been argued by some economists that Arrow's impossibility theorem constitutes an insuperable barrier to the moral justification of democracy. Those who do not subscribe to this view contends that a more defensible conception of majority rule and the democratic process is that they provide for equal distribution of resources over collective decision making. A moral victory justification of democracy so conceived can be derived from defensible principles of justice, it has been argued by the critic of Arrow. Arrow's 1950 article and the 1951 book gave rise to much controversy.
Outside the above trio among early moderns, Joseph Schumpeter put forward another theory of democracy in which the social function of democracy is satisfied incidentally by the competitive struggle for power between parties, just as the social function of market is fulfilled by the competitive struggle for profits among firms (Capitalism, Socialism and Democracy, 1950). Anthony Downs ,a student of Arrow, developed Schumpeter's insight and demonstrated how political competition between parties could produce a welfare maximum and thus avoid the implications of Arrow's impossibility theorem. His attempts in this regard failed but he succeeded in developing a mode of analysis of competition using models that would have great impact on future studies in the field. Downs also developed a model of rational voter who rationally chose to remain ignorant of most of the issues in an election.
All the early moderns discussed above were economists. William Riker, a political scientist, made significant contribution to the discipline of public choice when he wrote his book 'The Theory of Political Coalition'(1962). In this book Riker developed the theory of coalition formation that explained why great coalitions did not last long.
Three more scholars can be included in the category of 'early moderns' if the period of overview is extended to the 1970s. First of these is Gordon Tullock, a lawyer by profession who took interest in public choice theory and collaborated for some time with James Buchannon. He published an article in 1967, the importance of which was late in recognition by economists working in the field. It was left to Anne Krueger and Richard Posner who used the main idea in Tullock's article and gave it the name of 'rent seeking'. Until Tullock's 1967 article, social costs of monopoly was measured in terms of lost consumers surplus, resulting from monopolist's restrictions on output. Tullock pointed out that the right to supply the monopolised product was a valuable right, and that individuals could be expected to invest time and money to obtain this right. According to Tullock, these investments constitute a pure social waste as they only serve to determine the identity of the monopoly rent recipient. He showed that the social costs of rent seeking were potentially very large. Most of the writings that followed Tullock and Anne Krueger's expositions analysed rent seeking as if it was only a problem of public sector whereas the logic of the phenomenon applies equally to private sector.
If Tullock's rent seeking article was a 'hidden classic', as it came to be anointed later, Amartya Sen's article (1970) on social choice has been termed as an 'unassuming classic'. Following in the trail of Arrow's impossibility theorem and the paradox it represents, Sen introduced another set of paradox.
Where Arrow had sought to prove that it was impossible not to have a dictator and four of the criteria mentioned by him, Sen contended that it was impossible to allow someone to be a dictator over even one simple choice and satisfy three other criteria.
The last contribution to public choice theory among the early moderns includes Niakenen whose book on bureaucracy (1971) applied public choice theory to this institution of government. His thesis was that bureaucrats seek to maximise the size of their budget and then proceed to enjoy the benefits of this. His book presaged a burgeoning literature on the subject.
LATE MODERNS: During the 1970s several papers were published, extending the implications of Arrow's impossibility theorem. Satterhwaite (1976) and Gibbard (1977) demonstrated the impossibility of having a preference aggregation procedure that was both non-dictatorial and strategy-proof, where strategy-proof meant that everyone's best strategy was to faithfully reveal their true preferences. These theorems showed the close relationships between Arrow's alternative axiom and the goal of having a preference aggregation procedure in which individuals did not have an incentive to behave strategically.
Mckelvey (1976) and Schofield (1978) based their work on Arrow's theorem and rung down the curtain on his work, so to say. Their theorems painted a very negative picture of the capacity for democratic procedure to aggregate information on voter preferences. They showed that collective decisions were likely to be arbitrary and dictatorial. Free riding and the strategic concealment of individual preferences undermined democracy's legitimacy, they argued. Rent seekers, including bureaucracy, constituted the waste of democracy.
Populists aspiring to aggregation of individual preferences through democracy was attacked by William Riker who in his book (1982) explained why it was not possible. Prior to his book several works on public choice had painted a cheerful picture of democracy's potential in this regard.
After Paul Samuelson had shown (1954) that it would be impossible get people to reveal their preferences, Clarke (1971) and Groves (1973) demonstrated that people could be induced to reveal their preferences for public good by charging them a special incentive tax. The tax would be equal to the costs that their participation in the collective choice process imposed on other voters .This procedure has come to be known as 'demand revelation process'.
Mueller (1978) showed that the preference revelation problem could be solved using a three-step procedure in which each individual first makes a proposal and then following a random determination of an order of veto voting, removes in element from the set of all proposals.
DECADE OF EIGHTIES: During the '80s several papers were published suggesting that two-party representative governments were far better at aggregating individual preferences than had previously been shown to be the case. One set of these articles simply denied the assumption of the voter model that each individual votes with probability one for the candidate promising a higher utility. Instead the accepted assumption is that the probability of an individual voting for a candidate increases when the candidate promises a higher utility. Substituting this probabilistic voting assumption allowed Coughlin (1984) and Nitzen (1981) to prove that the competition for votes between two candidates led them to select an equilibrium pair platform that maximised some form of social welfare function. Schumpeter's assertion that the competition for votes between parties resulted in a form of 'invisible hand theorem' for the public domain was thus finally proved, though it had to wait for 40 years.
In the case of a multi-dimensional issue, every choice of platform by one party can be defeated by an alternative choice of platform by the other and the two candidates may 'cycle' endlessly under the assumption of deterministic voting. Such cycling could in theory take the candidate far away from the set of most preferred points of the electorate. These results sound a more optimistic note about the potential for preference aggregation than many of the works discussed earlier.
EMPIRICAL WORKS: All the early works on public choice have been theoretical in nature. As the field of enquiry and analysis matured an increasing number of studies have been published for testing theories. Some of these empirical studies are discussed below.
One of the frequently mentioned propositions of Anthony Downs (1957) is that parties formulate policies to win elections, rather than win elections in order to formulate policies. Among the policy of great concern to voters few are more important than the state of the economy. If Down's proposition is correct then parties should compete for votes on the basis of their promised macro-economic policies and both parties in a two-party system should offer the same set of policies. Kremar (1971) was the first to test a relationship between the state of the economy and votes for members of parliament and president. Nordhaus (1975) and MacRae (1977) were the first to develop a Downsian model of the 'political business cycle' in which both parties are predicted to follow the same strategy of reducing unemployment going into an election to induce short-sighted voters to vote for the incumbent party.
Observers of politics in America and the United Kingdom (UK) have questioned the prediction of the one-dimensional Downsian model that both parties adopt identical positions at the most-preferred outcome for the median voter. This prediction appears to be heavily at odds with the evidence concerning macro-economic policies, where right-of-centre parties seem to be more concerned with inflation, while left-of-centre parties appear to attach priority to employment. Writings by Hobbs (1977; 1987) and Frey and Schneider (1978) incorporated these 'partisan effect' into a political model of macro-economic policy and provided empirical evidence in support.
In some areas of public choice studies, data for testing propositions or hypothesis are scarce and difficult to come by. This limits the number and scope of empirical works in this field. Some scholars have tried to get around this problem by undertaking studies in hypothesis that link policy choices to political or macro-economic outcomes. Facts and figures on election results and data on macroeconomic variables are available in almost all countries. This has made it possible to test hypothesis of researchers or to re-test or refine previously used hypothesis in studies conducted in the past.
As a result, literature on 'political business cycle' has been growing at a healthy rate, particularly in America and the UK. The main findings of these empirical studies are that in a two-party polity, partisan differences across parties are both significant and persistent. But it is also seen that both the parties of the right and the left tend to become more 'Downsian' as an election approaches and adopt their policies to appeal to middle -of-the road voters.
In respect of 'political business cycle' studies, the literature on representative government (democracy) is based more on two-party systems, neglecting multi-party systems. To redress this imbalance public choice studies on multi-party countries have belatedly seen an upward trend, taking up cases in Europe and some in Latin America.
A common feature in the public choice studies of multi-party systems is that no single party typically wins a majority of seats in the parliament and thus no single party is able to form a government. Consequently, a coalition of parties is cobbled together to form government. Alternatively, a minority government is formed. In either case, instability becomes the order of the day, making long term policy formulation difficult. Promises made to voters remain unfulfilled making short shrift of aggregation of individual preferences. What is worse, such governments are very often short-lived.
Public choice studies of 'political business cycle' under multi-party system in fragile democracies like Bangladesh have not been noticeably undertaken either by Bangladeshi or foreign scholars. But books and articles on politics, even political economy, are quite popular, to judge by their numbers in the market. Very few, almost none, of these writings have used the discipline of public choice.
CONCLUSIONS: It is more than 80 years that public choice studies began as an inter-disciplinary study. A vast body of literature has grown up over the years, embodying both theoretical and empirical works. The last category has lately been enriched with hypothetical case studies. Overwhelming majority of works in the field has been by scholars of developed countries, particularly America and the UK. In respect of subjects, there is again overwhelming preponderance of two-party systems as noted above. If studies on political economy is not only for advancement of knowledge for the denizens of academia, there is a strong case for these studies to be undertaken in the context of developing countries like Bangladesh where their findings can be used for strengthening democracy and its institutions. It cannot be that academics from developing countries who return with degrees awarded to them in universities in the West are intellectually unable to take up studies about which they are informed and taught abroad. What is lacking must be motivation.
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