Periodic Reporting for period 2 - PRAGMA (Pragmatics of Multiwinner Voting: Algorithms and Preference Data Analysis)
Reporting period: 2022-12-01 to 2024-05-31
The PRAGMA project is in the area of computational social choice, an
interdisciplinary field of study focused on computational analysis of
group-decision making, with a particular focus on voting and
elections. The project has two main goals: The first one is to adapt,
develop, and extend the theory of multiwinner voting---i.e. the
theory of choosing committees---so that it would move from being a
convenient mathematical abstraction to being a viable tool for
applications. The second one is to build better understanding of
preference data, with a focus on the type of data that appears in
multiwinner voting. This way the second goal is facilitating the
progress on the first one, by allowing the discovered results to be
tested on realistic data. The main vision is to enable the use of
fair, efficient, explainable multiwinner voting mechanisms by
societies, institutions, and algorithm designers alike.
Examples of multiwinner elections that PRAGMA focuses on include,
e.g. choosing committees to perform particular tasks, choosing
members of universities' senates, choosing projects to fund within
participatory budgeting exercises in cities, as well as virtual
elections that could help in designing better search
algorithms. Indeed, many real-life elections are carried out using
suboptimal voting rules. For example, a university might be using a
voting rule that does not ensure proportional representation of its
members in the senate, a city might be using a participatory budgeting
rule which disenfranchises large groups of voters (in fact, such rules
are very common in practical participatory budgeting scenarios), and a
search engine might be giving insufficiently diverse results to its
users. The goal of the PRAGMA project is to offer voting rules and
means of using them that would avoid these problems and that would
both easy to use and to understand.
To achieve these goals, PRAGMA is strongly focused on understanding
the voting data. For example, it is important to know the types of
votes that appear in participatory budgeting scenarios, to analyze how
different voting rules differ from each other in practice. To this
end, a goal of the PRAGMA project is to develop a technique for
analyzing and visualizing election data, by means of similarity
analysis. The idea is that this will enable us to evaluate how similar
is the data generated using synthetic models to real-life one, and to
optimize these models.
Issues that PRAGMA is dedicated to solving are important to the
society because they are at the foundation of democratic processes.
With better voting tools, institutions will be able to make better
decisions. Improved participatory budgeting mechanisms will help
cities develop faster and people feel more involved. Better
algorithmic tools will lead to more fair, more useful search and
recommendation engines. Finally, better understanding of voting data
will be useful both internally within the project, but also beyond,
for follow-up research on the nature of democracy.
interdisciplinary field of study focused on computational analysis of
group-decision making, with a particular focus on voting and
elections. The project has two main goals: The first one is to adapt,
develop, and extend the theory of multiwinner voting---i.e. the
theory of choosing committees---so that it would move from being a
convenient mathematical abstraction to being a viable tool for
applications. The second one is to build better understanding of
preference data, with a focus on the type of data that appears in
multiwinner voting. This way the second goal is facilitating the
progress on the first one, by allowing the discovered results to be
tested on realistic data. The main vision is to enable the use of
fair, efficient, explainable multiwinner voting mechanisms by
societies, institutions, and algorithm designers alike.
Examples of multiwinner elections that PRAGMA focuses on include,
e.g. choosing committees to perform particular tasks, choosing
members of universities' senates, choosing projects to fund within
participatory budgeting exercises in cities, as well as virtual
elections that could help in designing better search
algorithms. Indeed, many real-life elections are carried out using
suboptimal voting rules. For example, a university might be using a
voting rule that does not ensure proportional representation of its
members in the senate, a city might be using a participatory budgeting
rule which disenfranchises large groups of voters (in fact, such rules
are very common in practical participatory budgeting scenarios), and a
search engine might be giving insufficiently diverse results to its
users. The goal of the PRAGMA project is to offer voting rules and
means of using them that would avoid these problems and that would
both easy to use and to understand.
To achieve these goals, PRAGMA is strongly focused on understanding
the voting data. For example, it is important to know the types of
votes that appear in participatory budgeting scenarios, to analyze how
different voting rules differ from each other in practice. To this
end, a goal of the PRAGMA project is to develop a technique for
analyzing and visualizing election data, by means of similarity
analysis. The idea is that this will enable us to evaluate how similar
is the data generated using synthetic models to real-life one, and to
optimize these models.
Issues that PRAGMA is dedicated to solving are important to the
society because they are at the foundation of democratic processes.
With better voting tools, institutions will be able to make better
decisions. Improved participatory budgeting mechanisms will help
cities develop faster and people feel more involved. Better
algorithmic tools will lead to more fair, more useful search and
recommendation engines. Finally, better understanding of voting data
will be useful both internally within the project, but also beyond,
for follow-up research on the nature of democracy.
The work within the PRAGMA project falls into two main categories: The
first one regards various ways of facilitating the use of multiwinner
elections, and the second one regards building the ``map of
elections'' for preference data analysis. Below we provide the
project's main achievements.
One important issue regarding multiwinner elections is explaining the
results to both voters and the candidates. Indeed, many multiwinner
rules, such as the single transferable vote rule (STV), do not even
have a naturally defined score, and those rules that do, such as
Proportional Approval Voting (PAV) only provide scores for the whole
committees and not for individual candidates. Hence, within PRAGMA we
have developed a technique for analyzing the performance of individual
participants. The idea is to measure the probability that a particular
person would enter the winning committee, depending on the amount of
random noise introduced in the votes. We have evaluated the
computational complexity of computing our measures and analyzed how
useful would be the provided information in practice. In particular,
we have evaluated our approach on a number of real-life participatory
budgeting scenarios. This research also motivated the study of ties in
multiwinner elections. Indeed, ties represent an extreme situation
where some candidates do not enter the winning committee even though
they could have, depending on the tie-breaking rule. We have obtained
a number of algorithms for detecting ties (which, in multiwinner
elections is far from trivial and can lead to intractable problems)
and we have evaluated probabilities of ties under various assumptions
regarding the distribution of the votes. Somewhat surprisingly, ties
are relatively likely to occur and, so, our algorithms for detecting
them are practically relevant. Additionally, we have shown that
multiwinner voting algorithms can be used to extend diversity in
results offered by recommendation systems (by designing a prototype of
a such a system for movies).
In terms of data analysis, the most important achievement of the
PRAGMA project is developing the ``map of elections'' framework. The
idea is to collect election instances (either those from repositories
of real-life ones or generated synthetically), compute distances
between them, and, based on that, analyze similarities between
them. This, however, requires so-called isomorphic distances, which
are invariant to candidate and voter identities. Within PRAGMA, we
have developed and analyzed such distances, and used them to analyze
elections. This lead to developing new, more realistic models of
generating synthetic election data for simulations, better
understanding existing models (which includes identifying and fixing a
possible flaw in one of the classic models), and better understanding
existing data. A side effect of our efforts is providing an analysis
of data from a number of participatory budgeting scenarios. These
results proved useful in convincing several cities to adopt the Method
of Equal Shares (MES) in their participatory budgeting efforts (MES is
a novel, proportional rule, far more fair than the typically used one,
as shown in our analysis).
first one regards various ways of facilitating the use of multiwinner
elections, and the second one regards building the ``map of
elections'' for preference data analysis. Below we provide the
project's main achievements.
One important issue regarding multiwinner elections is explaining the
results to both voters and the candidates. Indeed, many multiwinner
rules, such as the single transferable vote rule (STV), do not even
have a naturally defined score, and those rules that do, such as
Proportional Approval Voting (PAV) only provide scores for the whole
committees and not for individual candidates. Hence, within PRAGMA we
have developed a technique for analyzing the performance of individual
participants. The idea is to measure the probability that a particular
person would enter the winning committee, depending on the amount of
random noise introduced in the votes. We have evaluated the
computational complexity of computing our measures and analyzed how
useful would be the provided information in practice. In particular,
we have evaluated our approach on a number of real-life participatory
budgeting scenarios. This research also motivated the study of ties in
multiwinner elections. Indeed, ties represent an extreme situation
where some candidates do not enter the winning committee even though
they could have, depending on the tie-breaking rule. We have obtained
a number of algorithms for detecting ties (which, in multiwinner
elections is far from trivial and can lead to intractable problems)
and we have evaluated probabilities of ties under various assumptions
regarding the distribution of the votes. Somewhat surprisingly, ties
are relatively likely to occur and, so, our algorithms for detecting
them are practically relevant. Additionally, we have shown that
multiwinner voting algorithms can be used to extend diversity in
results offered by recommendation systems (by designing a prototype of
a such a system for movies).
In terms of data analysis, the most important achievement of the
PRAGMA project is developing the ``map of elections'' framework. The
idea is to collect election instances (either those from repositories
of real-life ones or generated synthetically), compute distances
between them, and, based on that, analyze similarities between
them. This, however, requires so-called isomorphic distances, which
are invariant to candidate and voter identities. Within PRAGMA, we
have developed and analyzed such distances, and used them to analyze
elections. This lead to developing new, more realistic models of
generating synthetic election data for simulations, better
understanding existing models (which includes identifying and fixing a
possible flaw in one of the classic models), and better understanding
existing data. A side effect of our efforts is providing an analysis
of data from a number of participatory budgeting scenarios. These
results proved useful in convincing several cities to adopt the Method
of Equal Shares (MES) in their participatory budgeting efforts (MES is
a novel, proportional rule, far more fair than the typically used one,
as shown in our analysis).
Some of the most exciting progress that we expect within PRAGMA
regards data analysis and the ``map of elections'' framework. While
the framework was developed for elections, we have already been able
to apply it to, e.g. stable roommates problems and to voting rules
themselves. We expect that the idea of visualizing relations between
both synthetic and real-life instances of various problems will also
find applications in other domains (for example, regarding problems of
fair resource allocation or regarding the analysis of various kinds of
tournaments). We expect that it will have strong effect on
experimental studies regarding these problems. In parallel, we also
seek results that would allow us to better understand the framework
itself, e.g. by looking for techniques for identifying areas of the
maps without known instances. Such techniques would allow us to find
types of instances on which given algorithms were not tested yet and,
hence, would lead to better evaluation of these algorithms.
Further, the introduction of isomorphic distances allowed us to
develop a new technique for learning parameters of statistical
distributions. We expect that in the future we will enhance our
techniques and extend them to be applicable to more types of data (such
as approval elections that appear in participatory budgeting settings)
and to more involved distributions (such as mixture models).
We also invest significant effort into developing algorithmic
infrastructure that would facilitate running participatory budgeting
elections. This includes, e.g. seeking results that would explain the
strategies that project proposers should take to have greatest chance
in getting their projects funded or developing techniques for
explaining election results. Indeed, fair budgeting rules, such as
Method of Equal Shares (MES), may generate result that at first sight
appear surprising (such as funding a more expensive project that is
supported by fewer voters instead of a cheaper one, with greater
support). Such situations, however, are natural and we seek algorithms
that would automatically provide arguments as to why this is so (in
the given example, it might be because the cheaper project is
supported by voters who already got even more appealing projects,
whereas those supporting the more expensive ones would, otherwise, be
left with no project that they like).
Altogether, we expect that by the end of the project, we will have a
set of algorithms that will make it easy to run fair, convincing
participatory budgeting elections (as well as other types of
elections, ranging from small scale ones in institutions to virtual
ones, held within computer systems). The algorithms will allow both to
generate realistic data (e.g. for evaluation and testing), compute
election results, and explain these results, if needed.
regards data analysis and the ``map of elections'' framework. While
the framework was developed for elections, we have already been able
to apply it to, e.g. stable roommates problems and to voting rules
themselves. We expect that the idea of visualizing relations between
both synthetic and real-life instances of various problems will also
find applications in other domains (for example, regarding problems of
fair resource allocation or regarding the analysis of various kinds of
tournaments). We expect that it will have strong effect on
experimental studies regarding these problems. In parallel, we also
seek results that would allow us to better understand the framework
itself, e.g. by looking for techniques for identifying areas of the
maps without known instances. Such techniques would allow us to find
types of instances on which given algorithms were not tested yet and,
hence, would lead to better evaluation of these algorithms.
Further, the introduction of isomorphic distances allowed us to
develop a new technique for learning parameters of statistical
distributions. We expect that in the future we will enhance our
techniques and extend them to be applicable to more types of data (such
as approval elections that appear in participatory budgeting settings)
and to more involved distributions (such as mixture models).
We also invest significant effort into developing algorithmic
infrastructure that would facilitate running participatory budgeting
elections. This includes, e.g. seeking results that would explain the
strategies that project proposers should take to have greatest chance
in getting their projects funded or developing techniques for
explaining election results. Indeed, fair budgeting rules, such as
Method of Equal Shares (MES), may generate result that at first sight
appear surprising (such as funding a more expensive project that is
supported by fewer voters instead of a cheaper one, with greater
support). Such situations, however, are natural and we seek algorithms
that would automatically provide arguments as to why this is so (in
the given example, it might be because the cheaper project is
supported by voters who already got even more appealing projects,
whereas those supporting the more expensive ones would, otherwise, be
left with no project that they like).
Altogether, we expect that by the end of the project, we will have a
set of algorithms that will make it easy to run fair, convincing
participatory budgeting elections (as well as other types of
elections, ranging from small scale ones in institutions to virtual
ones, held within computer systems). The algorithms will allow both to
generate realistic data (e.g. for evaluation and testing), compute
election results, and explain these results, if needed.