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Approval Voting by Brams, Steven, Fishburn, Peter C. [Springer, 2007] (Paperback) 2nd Edition [Paperback]
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July 13, 2024
For 5+ decades now, I have been studying voting schemes in connection with reliable computer systems using multiple independent computation channels. More recently, I have expanded my studies to voting in sociopolitical contexts, hoping that the expanded view might offer applications and benefits to reliable computing.
Voting is quite simple when we have only two candidates, but having 3+ candidates can give rise to anomalies and improper results. Consequently, mathematicians and social scientists have been studying many different voting schemes in order to minimize such anomalies and improper results. Plurality voting, the one we use most widely, is particularly prone to undesirable effects such as vote-splitting and spoiler candidates. When combined with a second-round run-off election, problem cases subside, but they don't completely go away.
In approval voting, a voter isn't forced to just pick one candidate, his/her most-preferred, but can "approve" any number of candidates. Each approved candidate receives one vote, and the candidate with the most vote wins. Vote-splitting does not occur, because a voter may approve more than one candidate, so s/he won't be forced to choose between his/her first and second choices, say. Similarly, spoiler candidates, who have virtually no chance of being elected, won't take away votes from mainstream choices.
There is a theoretical "impossibility" result, known as Arrow's Theorem, that shows no voting scheme is perfect, in that, given any voting scheme, we can construct examples to violate one or more of the axioms of "good" voting schemes. Approval voting, the subject of this book, comes close to being an ideal voting scheme.
Chapter 1 of the book offers a wrap-up summary of the main ideas in simple, non-mathematical terms. The casual reader will be convinced by the arguments and discussions in Chapter 1 that approval voting is better than plurality voting, even when a run-off round is added to the latter. The remaining 9 chapters get quite mathematical, which may not be to some readers' liking.
To apply voting schemes in the sociopolitical context, we need practicality in addition to scientific merit. Approval voting isn't much more difficult to implement than plurality voting. Existing voting technology, perhaps with small modifications, would suffice. Plurality voting is also easily understood by voters, and is thus unlikely to cause confusion.
We have no choice but to update our laws and procedures, as we uncover their flaws and learn about doing things more logically. Approval voting appears to strike a reasonable balance between mathematical guarantees of appropriate behavior and practicality of implementation.
I will end this review with a quote from an 1816 letter of Thomas Jefferson to Samuel Kerchaval: "I am not an advocate for frequent changes in laws and constitutions, but laws and institutions must go hand in hand with the progress of the human mind. As that becomes more developed, more enlightened, as new discoveries are made, new truths discovered and manners and opinions change, with the change of circumstances, institutions must advance also to keep pace with the times."
[P.S.: The authors state that they have changed very little in the book's second edition, aiming only to correct minor errors in the original text, in part because Brams discusses recent research on approval voting in Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures, with key elements also appearing in the authors' joint journal articles.]
Voting is quite simple when we have only two candidates, but having 3+ candidates can give rise to anomalies and improper results. Consequently, mathematicians and social scientists have been studying many different voting schemes in order to minimize such anomalies and improper results. Plurality voting, the one we use most widely, is particularly prone to undesirable effects such as vote-splitting and spoiler candidates. When combined with a second-round run-off election, problem cases subside, but they don't completely go away.
In approval voting, a voter isn't forced to just pick one candidate, his/her most-preferred, but can "approve" any number of candidates. Each approved candidate receives one vote, and the candidate with the most vote wins. Vote-splitting does not occur, because a voter may approve more than one candidate, so s/he won't be forced to choose between his/her first and second choices, say. Similarly, spoiler candidates, who have virtually no chance of being elected, won't take away votes from mainstream choices.
There is a theoretical "impossibility" result, known as Arrow's Theorem, that shows no voting scheme is perfect, in that, given any voting scheme, we can construct examples to violate one or more of the axioms of "good" voting schemes. Approval voting, the subject of this book, comes close to being an ideal voting scheme.
Chapter 1 of the book offers a wrap-up summary of the main ideas in simple, non-mathematical terms. The casual reader will be convinced by the arguments and discussions in Chapter 1 that approval voting is better than plurality voting, even when a run-off round is added to the latter. The remaining 9 chapters get quite mathematical, which may not be to some readers' liking.
To apply voting schemes in the sociopolitical context, we need practicality in addition to scientific merit. Approval voting isn't much more difficult to implement than plurality voting. Existing voting technology, perhaps with small modifications, would suffice. Plurality voting is also easily understood by voters, and is thus unlikely to cause confusion.
We have no choice but to update our laws and procedures, as we uncover their flaws and learn about doing things more logically. Approval voting appears to strike a reasonable balance between mathematical guarantees of appropriate behavior and practicality of implementation.
I will end this review with a quote from an 1816 letter of Thomas Jefferson to Samuel Kerchaval: "I am not an advocate for frequent changes in laws and constitutions, but laws and institutions must go hand in hand with the progress of the human mind. As that becomes more developed, more enlightened, as new discoveries are made, new truths discovered and manners and opinions change, with the change of circumstances, institutions must advance also to keep pace with the times."
[P.S.: The authors state that they have changed very little in the book's second edition, aiming only to correct minor errors in the original text, in part because Brams discusses recent research on approval voting in Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures, with key elements also appearing in the authors' joint journal articles.]
August 15, 2012
A review of this book is forthcoming.
Displaying 1 - 2 of 2 reviews