There has been a great deal of work on voting science over the past
~200 years. Unfortunately, the conclusions are "it depends". Is the
system you describe better than the current system? It depends on what
is considered important.

Here is a summary of vote aggregation methods and some ways to measure
their efficiency and fairness:

  http://lorrie.cranor.org/pubs/diss/node4.html

Excerpt:

     The paradox of voting is the coexistence of coherent individual
valuations and a collectively incoherent choice by majority rule. In an
election with three or more alternatives (candidates, motions, etc.)
and three or more voters, it may happen that when the alternatives
are placed against each other in a series of paired comparisons, no
alternative emerges victorious over each of the others: Voting fails to
produce a clear-cut winner.

    William H. Riker, 1982 [86] 

The paradox of voting was discovered over 200 years ago by M. Condorcet,
a French mathematician, philosopher, economist, and social scientist.
However, it received little attention until Duncan Black [13] explained
its significance in a series of essays he began in the 1940s. The
importance of the voting paradox was not fully realized until several
years after Kenneth Arrow published Social Choice and Individual Values
[3] in 1951, which contained his General Possibility Theorem. The
essence of this theorem is that there is no method of aggregating
individual preferences over three or more alternatives that satisfies
several conditions of fairness and always produces a logical result.
Arrow's precisely defined conditions of fairness and logicality have
been the subject of scrutiny by other scholars. However, none have
found a way of relaxing one or more of these conditions that results
in a generally satisfactory voting system immune from the voting
paradox.  Thus Arrow's theorem has the profound implication that in many
situations there is no fair and logical way of aggregating individual
preferences -- there is no way to determine accurately the collective
will of the people.

Social choice theorists have invented many vote aggregation systems
and have attempted to determine the most appropriate systems for a
variety of voting situations. Although there is some agreement about
which characteristics are desirable in a vote aggregation system,
there is much disagreement as to which characteristics are most
important. In addition, the selection is often influenced more by
political circumstances than by the advice of theorists. Thus the
popularity of a voting system is not necessarily an indication of its
fairness [66].

The choice of a vote aggregation system can influence much more
than the results of an election. It can also influence the ability
of analysts to interpret election results, and in turn the ability
of representatives to understand the wishes of the people they
represent and the satisfaction of the electorate that they have had
the opportunity to express themselves. This is due to the fact that
the various vote aggregation systems require voters to supply varying
amounts of information about their preferences and that some systems
tend to encourage voters to report their preferences insincerely. In
addition, the choice of vote aggregation system could affect the
stability of a government, the degree to which an organization
embraces or resists change, and the extent to which minorities are
represented. It could also affect the ability of the members of an
organization to achieve compromise.

This section explores the many types of vote aggregation systems....


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