paradox" is another model which has been used
and studied to understand inefficiencies which exist in voting
and democracies. Democratic societies use ballot procedures to
determine aggregate preferences and to make the social decisions
that follow them. If all votes could be unanimous, efficient decisions
would be guaranteed. Unfortunately, unanimity is virtually impossible
to achieve when hundreds of millions of people, each with his
or her own different preferences, are involved.
The most common social decision-making mechanism is majority rule. However, this system is far from perfect. In a well-known work published in 1951, Kenneth Arrow proved what has been called the "impossibility theorem." With this he showed that it is impossible to devise a voting scheme that respects individual preferences and gives consistent, definite results.
The voting paradox is an example of
irrational results that can result from majority-rule voting.
Consider the following example: Suppose that, faced with a decision
about the future of a firm, the president of the company decides
to let her three top administrators vote on the following options:
the number of employees and hire more monitors (supervisors),
B) maintain the current size
of the supervisors and employees, or C)
cut back on supervisors and reduce the number of employees. The
Vice President of finance (VP1) prefers A to B and B to C. The
Vice President of hiring and firing (VP2) doesn't want to rock
the boat. She prefers keeping the current size of the firm (option
B) to either of the others, although she prefers C to A. The 3rd
in command does believe in changes and doesn't really care if
it means decreases or increases in things. He prefers C to A and
A to B.
When the three vote on
A vs B, they vote in favor of A-to increase the university size
because VP1 and the 3rd in command outvote VP2. Voting on B and
C gives B a victory over C. But then they all vote on A vs C.
Here a problem arises because C wins. But if A beats B, and B
beats C, how can C beat A? The results seem to be a bit inconsistent
don't you agree?!?
What this voting paradox
illustrates is that when preferences for public goods differ for
individuals, any system for adding up those preferences can often
lead to inconsistencies and results which just don't seem to make
much sense. The voter's paradox also shows us that when there
are more than 2 alternatives, we should not make paired comparisons,
to avoid mistakenly assuming that a chosen alternative is preferred
to one that is not chosen. We need to consider all the alternatives
together, because if we do this we might discover that the collective
may have no clear preference. What this also shows is that people
may then be able to sway the outcome of an election to their advantage;
specifically related to 1) agenda setting (on the
part of the candidates) and to 2) strategic
voting (on the part of the voters); which are both
inefficiencies and do occur. Much of the work that has been done
in these areas is very mathematical and complex, but let me just
give you an outline of the conclusions that have been drawn.
The idea of agenda
setting refers to the means of making decisions based
on the order in which issues or candidates will be compared. Clever
people will be assigned the task of setting the agenda for the
elections or meetings where incomplete pairwise comparisons are
held. If the preferences are such that a voters' paradox is present,
they can manipulate the agenda to obtain their preferred outcome.
voting refers to voting in a way which is different
from your preferences in order to cause a preferred alternative
to be chosen. In other words, you are treating the vote as a kind
of game in which you adopt the best strategy to win. It can be
a big threat to a system in which there are party primary elections.
In such elections, people may chose to vote for a candidate that
they know is most likely to be defeated in the general election
so that that party can win. When people can act in these ways,
it is obviously not efficient.
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