Letting History and Evolution and Math Teach Us How to Vote

Sometimes the only consolation I can drag myself towards–lying awake at night as I wonder at the financial and vocational vacuum that is a doctorate in the history of science—is that someday the questionably useful bits of knowledge I have accrued over the last ten years will provide a guide to the post-apocalyptic, raggedy remains of the human species starting from scratch after some unforeseeable Armageddon. My secret wish is thus that, somehow, the ghostly corpse of this website will be found amid the ruined digital landscape of the internet should some cataclysm befall human civilization and society need to hit the reset button.

One of the things that fascinates me about the world is the way nature, in unexpected ways, offers up wisdom if only we take the time to look for it. For instance, take voting for elected officials. Seemingly a straightforward process, but one with a complicated production running behind the scenes that must be accounted for. Close your eyes and imagine something for me: you and one hundred thousand of your closest friends are forced to rebuild the republic in theory and practice. How will you set up a voting system? What does it need to accomplish? How will it handle the capriciousness of the human animal? How will it deal with social interaction? Corruption? Idealism? Negligence? Apathy? Complex economic, cultural, religious, and political issues? How do you maximize happiness for everyone, even the losers? How do you protect the individual in the face of corporate interests s/he might not share? These are all incredibly important questions, and choosing a voting system is a serious business and should be done by serious people.



The Way We Vote Now

The way we vote today is called Plurality Voting. A ballot has x number of candidates, you choose the one you want to win. That’s how we’ve always done it, so what’s wrong with it? Turns out, almost everything.

History Teaches Us

The history of political elections in the United States, looked at with a critical eye, shows that Plurality Voting has ruined a great number of important elections through spoilers and vote splitters. Here are just a very few examples. 1) 1844: James K. Polk versus Henry Clay. 49.5 to 48.1. Spoiled by James Birney’s 2.3, which would have changed the electoral map and given the election to Clay. Clay was awesome, Polk a dufus.  2) 1848: Zachary Taylor versus Lewis Cass. Spoiled by Martin Van Buren. If 90% of Van Buren’s votes had gone to Cass (as they probably would have), you get the latter instead of Taylor. 3) Between the Civil War and WWI, Democrats won only three elections. At least two were the result of spoilers. Perhaps all three. Cleveland in 1884 and 1892, Wilson in 1912. 4) 1912 election is a classic case. Roosevelt serves as a spoiler to Taft, who loses to Wilson. Debs and Eugene Chafin, together getting ~7% of the vote, also screw things up. Who doesn’t want TR in there again? Well, lot’s of people, and me too. Still, it serves my larger point.

Here’s the takeaway: in all of these cases, the winner was not someone who a majority of the people wanted. Doesn’t matter if they were left or right on the current political spectrum, conservative or liberal, or cat worshippers. Yes, there’s still plenty wrong with a simple popular vote; that’s not my target today. Still, if a voting system should do anything, it should try to be loyal to the interests of the people it purports to measure. But how, you ask, could it be done differently? Easy.


So history tells us plurality voting stinks. In fact, aside from randomly choosing among a pool of candidates, PV ranks consistently among the worst-designed voting systems. Let’s choose a new one. Check out this handy table:[1]

bayesian regret voting systems

This table shows the six best options for voting systems out there (more obviously exist, and others are variants of these, but these are the ones that have gotten the most treatment and investigation by scholars). The takeaway is that each bar represents a value called Bayesian Regret (yes, yet another incarnation of Bayesian statistics–that omnipresent extension of propositional logic which seeks probable outcomes in given scenarios). Here, it’s a visual representation of the statistical breadth of unhappiness generated by participating in a voting system. The right side of each black horizontal bar, coincident with the arrow pointing towards “worse,” is the overall level of regret generated in a population when everyone tries to “game” the system and vote strategically. If everyone votes strategically (I express the strongest feelings for Kerry even though I don’t like him, because he’s the lesser of two evils, and he wins or loses), Plurality, Condorcet, and Instant Runoff all generate equal amounts of and the most regret (which makes perfect sense, mathematically, but that’s a different, less immediately interesting discussion). Borda fares better, but RANGE VOTING and Approval Voting are the clear winners.

Now flip the script. Everyone votes honestly (I express the strongest feelings for Perot even though I know he’s not going to win) and Plurality still sucks. Like, really bad. In fact, you’ll notice its black bar is the shortest of all except approval. That means, among many other mathy things, that it can’t really tell the difference if you are lying to it or not. And it should, because people are liars. Instant runoff, Condorcet, and Approval are better, Borda in second, and RANGE VOTING wins. In reality, you’re going to get people voting both ways, so we want a system that has the highest mean. That’s RANGE VOTING.


Ever used the Amazon rating scale? Or seen the one used by Consumer Reports? Had a GPA? All these are RANGE VOTING stripped down. RANGE VOTING is a ballot with candidates arranged in a matrix on a given scale (0-9 (or whatever) with 0 being “Poor” and 9 being “Great” or “Excellent”) with the numbers printed inside the box, where voters indicate their preference for each candidate by shading in the appropriate box. The winner is determined either by calculating the average or by adding up the total number of points.  It looks like this:[2]

range voting ballot

Mathematical Benefits of RANGE VOTING

But if Amazon uses it, it can’t be great, right? Please, don’t tell me we’re going to run presidential elections like we’re rating a give-gallon bucket of Preparation H. Did you not read the spoiler section above? Have you not lived during an election? Plurality Voting isn’t doing any better.

Assessments of RANGE VOTING have been around for decades, but was most recently articulated by Warren D. Smith, a mathematics PhD from Princeton who worked on the faculty at Temple University. In the year 2000 in response to the U.S. General Presidential Election, he ran computer-generated models with 200 voters and 5 candidates on a range of issues, with a range of “happiness” values assigned to each voter for each candidate (the most strenuous system the computers he had access to could handle at the time. Subsequent simulations with larger sample sizes have borne his data out). Taking into account varying levels of ignorance of the candidates, he concluded that RANGE VOTING offers a number of inarguably significant advantages over every other voting method. Since then, he has expanded his computer-generated simulations, running millions of total elections with all sorts of variants and variables. These, and independent others, have all confirmed his original findings that RANGE VOTING offers many advantages:

  1. First, it solves the problem of spoilers and vote splitting by allowing voters to express more nuanced and informative indices of preference, and by allowing voters to indicate equal levels of preference for multiple candidates.
  1. Second, it handles a range in the number of candidates equally well, since values assigned are independent of each other, as opposed to many other voting methods (including Plurality and Approval voting). Do you understand the significance of this? NO MORE TWO-PARTY SYSTEM. Which has the effect of making it *a lot* more expensive for corporations and private interests to run the political system.
  1. Third, RANGE VOTING minimizes Bayesian regret (the average unhappiness felt by voters whose candidates did not win, and who must live with the candidate who did). Whether voters vote honestly or strategically, RANGE VOTING performs at its worst equal to simple Approval Voting and at its best better than any other voting method at its best.
  1. Fourth, RANGE VOTING allows for quick and efficient voting, and is more accurate with a lower rate of failure than simple majority voting.

Perhaps most significantly, it can be done with 100% of the voting machines currently in use in the United States.

Say what?! Cross my heart, hope to die.

Nature Teaches Us

To date, the people most interested in replacing Plurality Voting with Range Voting have run millions of computer simulations that bear out the above conclusions. By comparison, we’ve seen that during the course of just 57 presidential elections that plurality voting sucks the big one. Let’s let nature help us out. It is a well-studied phenomenon that bees use what is effectively RANGE VOTING to make decisions about new nesting sites every single year. During the course of bee history, the species has run hundreds of trillions of elections. That’s hundreds. Of trillions. Trillions with a T. And they have succeeded (right up until the entrance of 20th c. humanity and its pesticides), without written language or calculus or all the mechanisms and accomplishments that make humans “higher” animals, more than 90% of the time according to entomologists.

Two (long) excerpts which explain in more detail:

Each spring, about half the inhabitants of each beehive leave with their queen to start a new hive, in a swarm usually containing between 2000 and 20000 bees. The most important decision they need to make is: where to build that new hive? The penalty for choosing poorly is large: they’ll die next winter, get eaten by a predator, be unable to raise as many larvae, need to do more work over the next year and thus suffer a large disadvantage relative to wiser bees, etc. They usually find about 20 different options within about 100 square kilometers, and about 90% of the time, the bee swarm succeeds in selecting (what appears to entomologists to be) the best one . . [How do they do it?] 1. Most of the bees in the swarm find a branch to hang from in an energy-conserving “beard” formation, then sit there. 2. About 5% or fewer of the bees go scouting. If they find one or more candidate nest sites, they (after carefully inspecting the site for a duration of around 1 hour) return to the swarm and “report” (via “dancing” using a kind of sign language) both (a) where the best one they found is, and (b) how good they think it is. Better sites get more repetitions of the dance, executed with more vigor. Dances for housing reports appear to use the same sign-language as dances for food-location reporting, but the housing-related dances are much longer, lasting minutes to hours, versus seconds to a few minutes for food-location dances. 3. Some bees who wish to be scouts observe these reports and fly out to check the alleged sites for themselves (as well as, perhaps, doing their own exploring). Also, some bees who already have been scouts can choose to re-explore their own sites or the sites advertised by others. In all cases they report back as before, but bees re-exploring their old favorites, then re-advertise them with successively fewer dance repetitions each time, and once they reach zero, they “reset” themselves to an unbiased state. 4. So after some time has elapsed, multiple “camps” of bee scouts emerge, each camp advertising different potential nest sites . . . As discovered by Kirk Visscher, the bees refuse to terminate an election until a “quorum” of at least 10-15 scout bees have explored a site, because otherwise (we presume) the quality of each site-evaluation would be too low.[3] 

When a group of honeybees are ready to create a new colony, thousands of bees, along with one queen, set off from their old hive. Scout bees are faced with the task of finding a suitable nest and reporting back to their group with the location of the best nest site; the information is communicated via the famous waggle dance. Unfortunately, the scouts don’t always agree on which site is best. So how does a swarm decide where to relocate? A group of researchers found that, upon returning to the swarm, scout bees will “headbutt” other scouts that are promoting a different nest site. This headbutt transfers a vibrational signal that, when repeated enough times, causes the other bee to stop dancing. Once a certain threshold is reached—that is, enough scouts that were advocating alternative sites have been headbutted into submission—the decision is made, and the swarm will move to the winning nest site.[4]

Concluding Thoughts

So why do we still use Plurality Voting? Because we’re lazy, uninformed, and apathetic. Explaining the benefits and ease of a change doesn’t lend itself well to thirty-second sound bites, or 5-minute interviews, or pamphlets in your mailbox. Tradition is a powerful driving force as well. Plus people’s eyes glaze over when they see math.

But the fact of the matter is, RANGE VOTING is just plain better. Now go out and change the way you vote in whatever organization you are a part of. Feel free to use this material whenever and wherever you want. Maybe toss a link my way if you do, if for no other reason than to be polite.

About the Author

Ry Marcattilio-McCracken has a PhD in the history of science, technology, and medicine. He writes at slowloris.scienceblog.comslowlorisblog.wordpress.com and tweets @slowlorisblog.

Further Reading


Poundstone, William. Gaming the Vote: Why Elections Aren’t Fair (And What We Can Do AboutThem). New York: Hill and Wang, 2008.

Seeley, Thomas D. Honeybee Democracy. Princeton: Princeton UP, 2010.

[1] image credit: Poundstone, William. Gaming the Vote: Why Elections Aren’t Fair (And What We Can Do About Them). New York: Hill and Wang, 2008.

[2] image credit: http://www.rangevoting.org/RangeVoting.html

[3] http://www.rangevoting.org/ApisMellifera.html

[4] http://arstechnica.com/science/2011/12/bees-reach-consensus-by-headbutting-dissenters/

The material in this press release comes from the originating research organization. Content may be edited for style and length. Want more? Sign up for our daily email.

6 thoughts on “Letting History and Evolution and Math Teach Us How to Vote”

  1. Macrocompression:

    The average person seems to have figured out amazon ratings, customer satisfaction surveys, and the nearly unlimited list of other everyday applications where we are asked to rank satisfaction on a scale of 1 to 10. To say that range voting is too complicated to implement understates the abilities of the average person and overstates the difficulty of completing a range voting ballot. Range voting just isn’t that complicated.

    I have major issues with your idea to weight the strength of a voter according to “how he has succeeded in life” (lets call this “Success” voting). Success voting is not a “voting system” in the way that Dr. Ry has used the term. It does nothing to address Bayesian regret or the host of other problems that come along with plurality voting. It could be implemented with any voting system, including plurality and range. Further, Success voting strikes me as arrogant and undemocratic. Who defines success? Based on the list you have provided you may as well start giving out additional votes to those fortunate enough to have been born into families with money.

    • Darrin: perhaps my explanation was not sufficiently clear, but the voting system I suggested is based on the amount that the individual has contributed to society in a practical (physical not financial) way. Then even a selfish and wealthy person who saves his money without giving to charity, would only be rated for very little in life and in his limited voting power.

      A poverty struck immigrant, whose efforts to help the community by a badly paid but useful job, and such a person who has many children, would be at the opposite end of the voting scale.

  2. Range voting system is a bit too involved for the average voter who must fill in too much of the matrix or table with numbers.

    The most ideal system is not always the most practical. Transferable voting systems where second and third choices may be introduced in cases where the first choice is wasted, may well prove to be a better system.

    One idea which really appeals to me is to weigh the strength of the voter according to how he has succeded in life.
    A person over age 16 (say) has 1 vote.
    A person who has completed 12 years of education gets another vote.
    Then its given greater votes for academic qualifications, marriage, parent-hood, service in the army or emergency services etc., with the final vote (seventh) for an unusually heroic act, rather like a Nobel Prize. This system is mentioned in a book by Nevile Shute, I think its called “In the Wet” a novel.

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