Participatory Budgeting and Beyond
Laurence L. Leff, Ph.D.
Associate Professor of Computer Science
Western Illinois University
(on sabbatical)
Based on genetic algorithms, as Figure One, we have
implemented a web system where participants decide on the
parameters for the United States Federal budget. There are
two phases: Each participant chooses the parameters for their
ideal budget. Then, each participant rates some of the other
participant’s budgets. The system uses these ratings to
select some to be crossed over. Steps Two through Five
repeat as shown in Figure One.
Conventional social choice functions choose a subset of or
rank the alternatives presented to the participants based on
their votes or input (Figure Two). In participatory budgeting,
the alternatives are relations; the output is a set of relations.
Figure One
In the case of the tax code, these would be a relation between
amounts of income, consumables, statuses such as citizenship,
deductables such as medical expenses and the
Figure One
amount of tax due. Based on the votes, some of the output
relations are selected from the input. Others are derived from one or more of the input
relations, and of course, the votes. Figure Three shows this paradigm. The output of the first
stage are the input alternatives on which the same voters would vote in the second round—
this process will repeat indefinitely or until convergence.
The manipulator choosing the weights for the budgets with which they were presented maps
to problems in quadratic and quartic programming.
Exploring the computational complexity of manipulation, simulations, game theory analysis
and implementation for human factors analysis will allow the demos to develop a complex
legal artifact, whether it be the tax system, a penal code or a constitution, without the benefit
of a representative body or other elite.