Utilitarian voting

By CLAUDE HILLINGER – Professor – University of Munich – Faculty of Economics

Combines and revises material from my previous two notes and takes account of comments.


Utilitarian voting (UV) and range voting (RV), or RVN all have the same meaning: cardinal aggregation of ballot scores, with the number of values on the voting scale left unspecified at this level of generality. There appears to be no agreement on the precise definition of 'N'. My preference is to let 'N' designate the number of values on the scale. Thus, approval voting (AV) with the scale {0, 1} would be UV2 or RV2.

Utilitarianism has been a prominent tradition in economic, political and philosophical thought for over 200 years. John Harsanyi, the most prominent theorist of utilitarian collective choice, has referred to "the utilitarian tradition, represented by Hume, Adam Smith, Bentham, John Stuart Mill, Sidgwick, Edgeworth and many others, including a number of contemporary philosophers and social scientists". (Harsanyi 1976, p. 37). A contemporary revival of utilitarianism is associated with the burgeoning interdisciplinary field of happiness research. Happiness researchers measure the determinants of individual happiness, or life satisfaction, on cardinal scales. They advocate utilitarian policies i.e. those that would increase average happiness as measured. Richard Layard, who summarizes this research, concludes: "We desperately need a concept of the common good. I can think of no nobler goal than to pursue the greatest happiness of all – each person counting." (Layard, 2005, p. 234). His book closes with a quotation from Jeremy Bentham.

Given the existence of an old and still vigorous tradition, I feel that those having a related agenda should associate themselves with the older tradition, rather than ignoring it. I will continue to refer to UV, but I have no problem with others preferring RV.

Utilitarianism, measurement and ideology: a historical note

The following is my own interpretation and not a standard account.

Utilitarianism is a doctrine formulated by Jeremy Bentham towards the end of the eighteenth century. The central postulate of utilitarianism is that the aim of government should be to maximize the general welfare, defined as the sum of individual utilities, a term coined by Bentham. Utilitarianism became the general philosophical background of classical economics. It shifted the focus of the subject away from the mercantilist concern with the treasury of the monarch, towards consideration of the welfare of the population. While the classical economists were convinced of the measurability of utility in principle, they took no steps in this direction.

With the advent of marginalism, utilitarianism became a victim of ideological battles. In order to discredit classical economics and advance their own agenda, the marginalists attacked utilitarianism as being an empty metaphysical theory. Their main argument was that the static theory of consumer demand did not require cardinal utility. Macroeconomics and welfare economics, the two principal areas that require cardinal measurement, were outside their focus.

A second attack on the idea of cardinal measurability of utilities came early in the twentieth century as a result of the conflict between orthodox economics and socialism. The socialists and their other allies on the left believed in the possibility and desirability of a strong state that would use scientific principles to achieve desirable social goals. They realized that such policies had to be based on measurement, with the result that there was an explosion of work on social and economic statistics. The answer of economic orthodoxy came in 1932 with Lionel Robbins' highly influential Scope and Method of Political Economy. Robbins reasserted the marginalist position that there was no scientific basis for the measurement of utility, and hence no basis for the socialist position that one could have scientific, and hence "value-free," policies that would maximize the aggregate welfare. Among economists it became a mantra to say "Of course, interpersonal comparisons of utility are impossible!" in order to signify one belonged to the orthodoxy.

Another dramatic turn in the ideological battles came at the Rand Corporation in the early days of the Cold War. The Rand Corporation, along with other American institutions, particularly the Ford Foundation, intended to fight communism not only militarily, but also on the ideological front. The most spectacular outgrowth of these efforts was Kenneth Arrow's 1951 Social Choice and Individual Values. Arrow was clearly inspired by Robbins, but where Robbins had merely made a claim, Arrow intended to offer a proof. The proof consisted of showing that a number of reasonable axioms regarding collective choice could not be simultaneously satisfied given that a cardinal representation of preferences was ruled out. By Arrow's own account, this result rules out not only rational collective decision making, but also the idea that markets produce rational solutions. The profound irony connected with this result is that, if taken seriously, it rules out capitalist democracy rather than, as intended, authoritarian communist planning.

Shortly after the publication of Arrow's result, Harsanyi published his demonstration of the fact that there is no difficulty in satisfying a set of Arrow-like plausible axioms on collective choice given that the cardinal representation of preferences is allowed. Strangely, Arrow's result established a vast literature on collective choice and more generally came to dominate the entire field of political theory. Harsanyi's work on collective choice was not followed up; his subsequent reputation, including him being awarded the 1994 Nobel Prize in Economics, instead was based mainly on his work on game theory.

My own work on utilitarian voting

Why should the RV community be interested in my work on UV, given that I have reached the same general conclusion? There are two basic kinds of reasons:

  1. I give a number of derivations of UV that are entirely different from the work on RV by Warren D. Smith. This should be of interest of itself. The fact that the theoretical derivations connect with the large literatures on collective choice and voting theories is also relevant. Finally, I give a pragmatic argument that connects with the large body of empirical work on the measurement of preferences.
  2. In addition to the general theory of UV, I have proposed the specific voting scale {+1, 0, -1} and refer to the use of this scale as "Evaluative Voting" (EV). It is an alternative to both AV and applied RV with its usual scales of {0,...,100} or {0,...,10}.

My involvement with voting theory has an unusual background. Early in my career as an economist I became aware of the dismal state of economic measurement and I traced it to the ideologically motivated aversion towards cardinal measurement described above. While there are many economic measures, such as real GDP, or consumer surplus, their conceptual foundation had remained foggy. I came to the conclusion that all of these measures must be interpreted as attempts at restoring the money metric when prices are variable. I interpreted the money metric as a "welfare indicator" that is applicable in a market context. With this background I realized that the equally disastrous state of voting theory had the same ideological origin in the rejection of cardinality.

On studying the theories of voting and of collective choice I came across a number of derivations that could be easily adapted to derive UV. The simplest, and the one I like best, is an adaptation of Harsanyi's derivation of utilitarian collective choice as the choice of a constitution behind a "veil of ignorance" regarding the issues that must be decided on in the future. If the constitutional choice under these conditions is the choice of a voting rule, and if voters can express their cardinal preferences on the ballot, then UV will maximize the expected utility that delegates to the constitutional convention can expect to gain in future elections. If the delegates are expected utility maximizers they will be unanimously in favor of UV. Other derivations can be found in the papers referred to in the references at the end of this note.

Important as the theoretical derivations are, I attach equal importance to a pragmatic consideration. The cardinal aggregation of preferences is in fact the basic tool of an entire industry. When firms or other organization want an evaluation of their services they ask their customers or clients to rate the various services offered on a cardinal scale. The scales may be directly expressed in numbers, or in evaluative words that are then converted to numbers. The same thing is done in political opinion polls and in the field of happiness research referred to above. It appears that the only area where preferences are aggregated without the use of simple cardinal scales is voting!

Those in a position to change voting rules are generally those who have been elected under the given rules to the top positions that the political system in question has to offer. It is not surprising that they have no interest in changing those rules!

Alternative scales

For political elections with a single winner I have proposed the scale {+1, 0, -1} to be interpreted as being for an alternative, neutral, or against it. My reasoning was that in political elections people are notoriously ill-informed so that they are hardly in a position to offer a more differentiated judgment. The wide swings in the popularities of politicians that are revealed by opinion polls also suggest that a more differentiated scale would hardly impart additional useful information. However, that people are sometimes favorably inclined towards some candidates, or issues, unfavorably towards others and indifferent towards still others is a common experience. I refer to voting with this scale as evaluative voting (EV).

Politics in most democracies has become more polarized in recent years. Radical parties or movements have been on the rise. At the same time political participation has been declining. I believe that many now apathetic voters would return to the polls if given a chance to vote against the politicians they most dislike. Politicians such as the xenophobic racist Le Pen in France, or parties like the neo-Nazi NPD in Germany would have much less of a chance if the broad majority that is opposed to them could express their dislike directly with a negative vote.

Voting theorists, socialized as they are into regarding voters as passionless, purely rational decision makers may be skeptical about this argument. I believe that many voters would appreciate the ability to cast a negative vote. As one contributor to a debate on approval voting wrote: "I would be much more comfortable with 'disapproval' systems where you mark against the ones you distrust... The list of names should be those who have alarmed us, not those who have impressed us with their ability to lay it on." (Hubley, 2001).

Approval voting has the scale {0, 1}. I agree that AV is much superior to PV. For the reasons given above, I think that EV is still superior.

RV, with the 0-100 "temperature" scale, or with a ten-point scale, raises different problems. Some voters may be unwilling to give the most preferred candidate the full 100 points because "he is not perfect." Meanwhile, others do so to maximize the power of their vote. I.e, the larger temperature scale provides more incentive for strategic voting, and hence falsification of preferences. Should election outcomes depend on such considerations?

Ask voters how they want to vote?

Voting is the most basic tool of democracy. The theoretical literature on collective choice and voting is immense but has reached no conclusion. The closest to a conclusion that has been reached was Arrow's claim that there is no solution! It would seem to be in the best democratic tradition to let voters themselves determine which system they want to use. One could have voters vote on the principal voting rules that have been proposed using these same rules in the process. It is quite possible, and I think even likely, that a "consensus" might emerge in the sense that all, or most of the voting methods would agree on a winner. I am not aware that any such study has ever been made. [Editor's note: unfortunately this consensus might not be the same in different places or different times. Referenda to change voting methods have had conflicting results.]


My papers on the subjects discussed above can be downloaded at:

The discussion of ideology in economics and political science is in:

It has also been published in the economics e-journal where it can be downloaded (and discussed) at

Regarding utilitarian voting, the most recent and complete paper is:
All of these papers contain references to the relevant literature.

Other References

Arrow, K. J. (1951), Social Choice and Individual Values, Wiley, New York. Second edition, 1963, Yale University Press.

Frey, Bruno S. and Stutzer, Alois (1999), Happiness and Economics: How the Economy and Institutions Effect Well Being, Princeton University Press, Princeton and Oxford.

Harsanyi, John C. (1976), Essays on Ethics, Social Behavior, and Scientific Explanation, D. Reidel, Dordrecht.

Hubley, Craig (2001), Psychological effects of approval voting, Letter to Science Magazine 292,5521 (12 June 2001) 1449.

Layard, Richard (2005), Happiness: Lessons from a New Science, London, Penguin Books.

Robbins, L. (1932), An Essay on the Nature and Significance of Economic Science, London, Macmillan. Third ed., 1984, New York University Press.

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