UTILITARIAN VOTING AND ITS SPECIAL CASES:
RANGE, EVALUATIVE AND APPROVAL VOTING
CLAUDE HILLINGER

PURPOSE
The purpose of this contribution is to acquaint the participants in
the range voting (RV) blog with my work on utilitarian voting (UV). I
will be discussing very fundamental issues related to voting theory
and a bit also to its history. Necessarily, this requires a longer
contribution than most.
DEFINITIONS
UV is the theory of voting under the assumption that voters are able
to express their evaluations of the alternatives on the ballot as
numbers that correspond to their cardinal utilities. The conclusion
of the theory, based on a variety of arguments, is that the winning
alternative should be that which maximizes the aggregate score, hence
the sum of utilities, and hence the name `utilitarian voting. The
general theory does not specify the scale to be used, specifically
the numbers that can be entered on the ballot. For general elections
I have proposed evaluative voting (EV) with the scale (+1, 0,-1) to
be interpreted as being for an alternative. neutral, or against it.
Approval voting (AV) has the scale (+1, 0). The abstract theory of RV
developed by Warren D. Smith, that leaves open the scale to be
employed, leads to the same conclusion UV and it could, in my view
should, have been given the same name. In practice, the advocates of
RV have used the `temperature scale' where the score can be any
integer in the range .

HISTORICAL BACKGROUND
Utilitarianism is the 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 the
maximization of the general welfare, defined as the sum of
individual `utilities', a term coined by Bentham. Utilitarianism
became the general philosophical background of classical economics
and shifted the focus of the subject away from the mercantilist
concern with the treasury of the monarch towards the 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 of thei 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 ones belonging 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 wanted 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 not difficulty in
satisfying a set of axioms analogous to those of Arrow 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 was not followed up; there is not even an entry under
his name in The New Palgrave.

I close this section with a note on terminology: For more than 200
years `utilitarian' has meant a method of arriving at a social
decision by maximizing the sum of cardinally expressed individual
preferences. My use of the term `utilitarian voting' conforms to this
usage. Inventing a new term `range voting' to refer to the same thing
violated the injunction of Occam's razor not to unnecessarily
multiply entities. For the remainder of this paper I will use `range
voting' to refer specifically only to voting with the temperature
scale.

MY OWN WORK: I. UTILITARIAN VOTING
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. It appears that the only
area where preferences are aggregated without the use of simple
cardinal scales is voting! How can this be explained? It's elementary
my dear Dr. Watson! 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 the rules!

MY OWN WORK: II. ALTERNATIVE SCALES
For general elections 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 general elections people are notoriously ill
informed so that they are hardly in a position to offer a more
differentiated judgment. 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.

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

RV, with the temperature scale, or with a ten point scale, raises a
different problem that has, as far as I know, not been discussed.
Whenever such scales are used in political opinion surveys, the
endpoints of the scales are rarely reported. The most preferred
candidate rarely gets 100 and the worst rarely gets 0. Evidently,
voters do not norm the scale to the alternatives at issue. 100 is the
score for an absolutely perfect candidate, who exists only in heaven.
0 is the score for the devil who mainly dwells in hell, though
putting in an occasional appearance on earth. The sincere vote of an
individual then depends on how distant a given candidate is on that
voters scale from being an angel or a devil. Consider an `idealist'
and a `realist' with the same ranking over a set of candidates. The
realist, more concerned with the existing world than with heaven or
hell, is likely to give his preferred candidate close to 100 and his
least preferred close to 0. Since the idealist considers a much wider
field of possibilities, including an angel and a devil, his ranking
of the alternatives will be much more towards the center of the
scale. Should election outcomes depend on such considerations?

Another problem with the temperature scale is that it provides an
incentive for strategic voting, and hence falsification of
preferences. The strategic voter has an incentive to maximize the
power of his vote by using the full scale. As is the case with all
forms of UV, the problem here is not as great as with some other
voting methods, since the voter has no incentive to change his
ranking of the candidates. Still, with RV, the problem is greater
than with EV or AV.

A SUGGESTED EXPERIMENT
Mathematicians have studied problems of voting for over 200 years and
in recent decades their numbers as well as the numbers of their
publications have exploded. All of this activity has not led to any
convergence of opinion among theoreticians and even less to an
improvement of practice. I suggest that it is time for a more
empirical and democratic approach. As a start I suggest an experiment
that could initially be carried out by participants of the RV-blog an
later hopefully in other venues.

The experiment is a vote involving the four methods: RV, EV, AV and
PV. The four methods would also be used in the votes. After the
closing of the elections, the participants could comment both
regarding the outcomes and regarding their feelings in using the
different methods in this election.

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

http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=191500

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

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=945947

Regarding utilitarian voting, the most recent and complete paper is:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=608821

All of these papers contain references to the relevant literature.