From 7a5f744ddf76cfc3c1f3f106c56833d1133a3862 Mon Sep 17 00:00:00 2001 From: Tobias Eidelpes Date: Thu, 14 May 2020 16:51:45 +0200 Subject: [PATCH] Add text for the preference elicitation models --- paper/references.bib | 31 ++++++++++++++- paper/termpaper.tex | 92 ++++++++++++++++++++++++++++++++------------ 2 files changed, 98 insertions(+), 25 deletions(-) diff --git a/paper/references.bib b/paper/references.bib index e7f2a76..cb1f982 100644 --- a/paper/references.bib +++ b/paper/references.bib @@ -40,6 +40,20 @@ series = {{{AAAI}}'17} } +@article{bogomolnaiaCollectiveChoiceDichotomous2005, + title = {Collective Choice under Dichotomous Preferences}, + author = {Bogomolnaia, Anna and Moulin, Herv{\'e} and Stong, Richard}, + year = {2005}, + month = jun, + volume = {122}, + pages = {165--184}, + doi = {10.1016/j.jet.2004.05.005}, + abstract = {Agents partition deterministic outcomes into good or bad. A mechanism selects a lottery over outcomes (time-shares). The probability of a good outcome is the canonical utility. The utilitarian mechanism averages over outcomes with largest ``approval''. It is efficient, strategyproof, anonymous and neutral. We reach an impossibility if, in addition, each agent's utility is at least 1n, where n is the number of agents; or is at least the fraction of good to feasible outcomes. We conjecture that no ex ante efficient and strategyproof mechanism guarantees a strictly positive utility to all agents, and prove a weaker statement.}, + journal = {Journal of Economic Theory}, + language = {en}, + number = {2} +} + @article{brandlFundingPublicProjects2020, title = {Funding {{Public Projects}}: {{A Case}} for the {{Nash Product Rule}}}, author = {Brandl, Florian and Brandt, Felix and Peters, Dominik and Stricker, Christian and Suksompong, Warut}, @@ -59,7 +73,7 @@ } @article{cabannesParticipatoryBudgetingSignificant2004, - title = {Participatory Budgeting: A Significant Contribution to Participatory Democracy:}, + title = {Participatory Budgeting: A Significant Contribution to Participatory Democracy}, shorttitle = {Participatory Budgeting}, author = {Cabannes, Yves}, year = {2004}, @@ -74,6 +88,21 @@ number = {1} } +@article{duddyElectingRepresentativeCommittee2014, + title = {Electing a Representative Committee by Approval Ballot: {{An}} Impossibility Result}, + shorttitle = {Electing a Representative Committee by Approval Ballot}, + author = {Duddy, Conal}, + year = {2014}, + month = jul, + volume = {124}, + pages = {14--16}, + doi = {10.1016/j.econlet.2014.04.009}, + abstract = {We consider methods of electing a fixed number of candidates, greater than one, by approval ballot. We define a representativeness property and a Pareto property and show that these jointly imply manipulability.}, + journal = {Economics Letters}, + language = {en}, + number = {1} +} + @inproceedings{fainCoreParticipatoryBudgeting2016, title = {The {{Core}} of the {{Participatory Budgeting Problem}}}, booktitle = {Web and {{Internet Economics}}}, diff --git a/paper/termpaper.tex b/paper/termpaper.tex index 21b4078..e456e54 100644 --- a/paper/termpaper.tex +++ b/paper/termpaper.tex @@ -13,7 +13,7 @@ \usepackage{hyperref} -\setstretch{1.05} +\setstretch{1.07} \addbibresource{references.bib} @@ -61,27 +61,27 @@ stages \autocite{participatorybudgetingprojectHowPBWorks}: \noindent The two last stages \emph{voting} and \emph{aggregating votes} are of main interest for computer scientists, economists and social choice theorists -because depending on how voters elicit their preferences (\emph{balloting}) and -how the votes are aggregated through the use of algorithms, the outcome is -different. For this paper it is assumed that the first three stages have already -been completed. The rules of the process have been set, ideas have been -collected and developed into feasible projects and the budget limit is known. To -study different ways of capturing votes and aggregating them, the participatory -process is modeled mathematically. This model will be called a participatory -budgeting \emph{scenario}. The aim of studying participatory budgeting scenarios -is to find ways to achieve a desirable outcome. A desirable outcome can be one -based on fairness by making sure that each voter has at least one chosen project -in the final set of winning projects for example. Other approaches are concerned -with maximizing social welfare or discouraging \emph{gaming the voting process} -(where an outcome can be manipulated by not voting truthfully; also called -\emph{strategyproofness}). +because depending on how voters elicit their preferences (\emph{balloting} or +\emph{input method}) and how the votes are aggregated through the use of +algorithms, the outcome is different. For this paper it is assumed that the +first three stages have already been completed. The rules of the process have +been set, ideas have been collected and developed into feasible projects and the +budget limit is known. To study different ways of capturing votes and +aggregating them, the participatory process is modeled mathematically. This +model will be called a participatory budgeting \emph{scenario}. The aim of +studying participatory budgeting scenarios is to find ways to achieve a +desirable outcome. A desirable outcome can be one based on fairness by making +sure that each voter has at least one chosen project in the final set of winning +projects for example. Other approaches are concerned with maximizing social +welfare or discouraging \emph{gaming the voting process} (where an outcome can +be manipulated by not voting truthfully; also called \emph{strategyproofness}). -First, this paper will look at how a participatory budgeting scenario can be -modeled mathematically. Then, a brief overview over common models will be given. -To illustrate these methods, one approach will be chosen and discussed in detail -with respect to algorithmic complexity and properties. Finally, the gained -insight into participatory budgeting algorithms will be summarized and an -outlook on further developments will be given. +First, this paper will give a brief overview of common methods and show how a +participatory budgeting scenario can be modeled mathematically. To illustrate +these methods, one approach will be chosen and discussed in detail with respect +to algorithmic complexity and properties. Finally, the gained insight into +participatory budgeting algorithms will be summarized and an outlook on further +developments will be given. \section{Mathematical Model} \label{sec:mathematical model} @@ -112,9 +112,53 @@ the degree of completion does not exceed the budget limit: \sum_{p\in A}{c(\mu(p))\leq B}. \end{equation} -\textcite{azizParticipatoryBudgetingModels2020} define a taxonomy of -participatory budgeting scenarios where projects can be either divisible or -indivisible and bounded or unbounded. +Common ways to design the input method is to ask the voters to approve a subset +of projects $A_v\subseteq P$ where each individual project can be either chosen +to be in $A_v$ or not. This form is called \emph{dichotomous preferences} +because every project is put in one of two categories: \emph{good} or +\emph{bad}. Projects that have not been approved (are not in $A_v$) are assumed +to be in the bad category. This type of preference elicitation is known as +approval-based preference elicitation or balloting. It is possible to design +variations of the described scenario by for example asking the voters to only +specify at most $k$ projects which they want to see approved ($k$-Approval) +\cite{goelKnapsackVotingParticipatory2019a}. These variations typically do not +take into account the cost that is associated with each project at the voting +stage. To alleviate this, approaches where the voters are asked to approve +projects while factoring in the cost have been proposed. After asking the voters +for their preferences, various aggregation methods can be used. +Section~\ref{sec:approval-based budgeting} will go into detail about the +complexity and axiomatic guarantees of these methods. + +One such approach, where the cost and benefit of each project is factored in, is +described by \textcite{goelKnapsackVotingParticipatory2019a}, which they term +\emph{knapsack voting}. It allows voters to express preferences by factoring in +the cost as well as the benefit per unit of cost. The name stems from the +well-known knapsack problem in which, given a set of items, their associated +weight and value and a weight limit, a selection of items that maximize the +value subject to the weight limit has to be chosen. In the budgeting scenario, +the items correspond to projects, the weight limit to the budget limit and the +value of each item to the value that a project provides to a voter. To have a +suitable metric for the value that each voter gets from a specific project, the +authors introduce different \emph{utility models}. These models make it possible +to provide axiomatic guarantees such as strategyproofness or welfare +maximization. While their model assumes fractional voting---that is each voter +can allocate the budget in any way they see fit---utility functions are also +used by \textcite{talmonFrameworkApprovalBasedBudgeting2019} to measure the +total satisfaction that a winning set of projects provides under an aggregation +rule. + +A third possibility for preference elicitation is \emph{ranked orders}. In this +scenario, voters specify a ranking over the available choices (projects) with +the highest ranked choice receiving the biggest amount of the budget and the +lowest ranked one the lowest amount of the budget. +\textcite{langPortioningUsingOrdinal2019} study a scenario in which the input +method is ranked orders and the projects that can be chosen are divisible. The +problem of allocating the budget to a set of winning projects under these +circumstances is referred to as \emph{portioning}. Depending on the desired +outcome, multiple aggregation methods can be combined with ranked orders. + +\section{Approval-based budgeting} +\label{sec:approval-based budgeting} \printbibliography