I'd put this together some years ago, before the rise of issues surrounding the elections in Florida and the 2000 US Presidential Election with Al Gore and George Bush.  After you read this, you may see how this system could have avoided some of the problems there (such as throwing out ballots where someone may have struck out a wrong vote and then added the right one, for example.)  But think about the following and consider what it may mean in a variety of elections you can imagine.  I think you'll agree that this method is a superior one in most details.

In the national election cycle for 2004, many Democrats were often upset about Ralph Nader running for president (and still are), as it's arguable that those who voted for Nader would have instead voted for the Democratic candidate were it that Nader wasn't running. Tensions between Democrats and those supporting Nader grew, particularly when Republicans involved themselves in trying to place Nader on voting ballots in several US States; and as the Democratic Party vigorously used what legal means it can muster to block the placement of Nader on US State ballots. The disgusting behavior of both major parties in the US was worthwhile to those two parties exactly because of our poorly designed voting system.

Frankly, I applaud having more parties involved. It bothers me that Nader was considered a threat by some, so much so that they'd wish our political choices were fewer, rather than more. I think he had every right to run -- if a system of democracy is to mean much at all, it must mean that we have options... and not always only two of them.

As things stand recently, we still have voting systems without good checks on their veracity; we still have many tens of thousands of dead voters showing up to vote; and there have been several serious investigations into the shape of our voting systems, all of them pointing out that the current situation simply isn't acceptable. The Report of the Commission on Federal Election Reform came out in September of 2005 and concludes that we need fundamental and systemic changes to our existing system. That's only the latest of several significant and comprehensive studies pointing out the urgent need for election reform.

Approval voting methods would remove this rancor and Ralph Nader (or anyone else, for that matter) could freely participate in our political processes without inspiring anger for their efforts from those supporting different candidates. It would encourage honest voting and remove these hostilities, too. Both, good things.

The original web page follows, with some final comments I have at the end of the page.

Sometimes, the results of our elections are confusing, particularly when there are more than two choices.  Hopefully, this article can help you understand why and offer perhaps one good way to improve things.

Introduction

Voting lies at the heart of representative government and participatory democracy. In fact, voting plays an essential role whenever control is shared and group choices about policy or action must be made. Party nominations, stockholder elections, economic goals, and community priorities are often decided through voting.

Voting is a solution to the problem of turning individual preferences for different outcomes into a single choice by the group as a whole. And although many procedures have been developed to reduce a list of alternatives to a desired option, it's surprising how few people realize that the method of voting they use can significantly impact the outcome of an election or just how likely it is to find that the selected person or issue doesn't actually hold a majority of the votes cast. And it's also true that a poorly chosen voting system can actually serve hidden ulterior motives of a few groups who can well enjoy the additional control and power it affords them, than would a voting system based on theoretical and dispassionate reasoning.

Before proceeding, realize that every voting method occasionally gives paradoxical results, so no one method is always best. Methods such as majority rule, plurality wins, elimination and runoffs, sequential pair-wise comparisons, various weighted or scoring schemes, approval voting, and a host of other partitioning schemes that choose between successive subsets of potential outcomes; all of these have situations where they choose poorly, some much more than others. The problem lies in choosing one that minimizes the chance of counter-intuitive results.

Although a perfect voting scheme is an impossible goal, it certainly isn't a waste of time trying to improve existing methods. For example, we all know that engines cannot perform with 100% efficiency, but that fact shouldn't stop the search for better efficiency and utility. Similarly, it's worthwhile to identify problems in the current tallying systems and to seek practical solutions.

Simple Isn't Always Good

Plurality voting is arguably the simplest method of selecting an outcome: everybody votes for their favorite choice and the choice with the most votes wins. But what about the case where there are 20 options to vote for and a winning plurality of only 6% succeeds. This is certainly a possible outcome for issues with factions of nearly equal size, but where one faction has a slight numerical advantage over the others. With 20 different options, and an average of 5% each, it's possible to see a 6% plurality win.

Now, of course this could be solved by successive runoffs where a few of the top choices are re-submitted to the voters. But consider another situation with only three possible outcomes: less taxes, the same taxes, and more taxes for everyone. Let's assume for the moment that the breakdown of support on these three outcomes is: 40%, 35%, and 25%, respectively.

If everyone votes their first choice, those wanting less taxes would win by plurality. But what if the voters already had a pretty good idea of the breakdown of support (for example, because of extensive polling results continually displaying these facts for all to see?) Wouldn't it make sense for those wanting more taxes to compromise their vote and side with those wanting to keep taxes the same? The outcome would then be to leave taxes alone - which is probably preferable for those wanting more taxes than would be allowing the "less-tax" group to win. Making this kind of calculation is called strategic or insincere voting. Of course, you already know that this kind of coalition voting actually happens!

A pure plurality system of voting generally performs so poorly with multiple choice questions that it is rarely used. More often, the choices are broken down into smaller groups (such as party members) that are offered in preliminary voting rounds (such as primaries) before a small set of choices (the candidates) are taken from the winners of the preliminary rounds and finally offered.

Rather than spend too much time beating up on one voting system though I'd like to describe a hypothetical case that illustrates a fundamental problem of voting methods. It'll be easier to see some of the issues surrounding the selection of voting systems. Also, please feel free to try out your own examples, whether made up or taken from real case histories, and see how they "play out." The example below is designed to illustrate and contrast several ideas into stark relief, but the general thrust of my comments will be born out as you try out your own cases, as well.

Take Your Pick

Let's assume that there are 55 delegates to a national, political party convention, at which five party members have been nominated to be the presidential candidate. We'll call the nominees, Alpha, Beta, Gamma, Delta, and Eta. Let's also assume that we've taken the time to individually poll each delegate, asking them to rank all five nominees according to his or her individual preferences. Although there are 120 conceivable distinct rankings (permutations) of the 5 different nominees, many fewer than that will arise in practice, because electors tend to split up into blocks of similar rankings. (Of course, it's also true that with only 55 delegates in this example, we'd only be able to get (at most) 55 distinct rankings.)  So, let's finally assume that the 55 delegates submit their preferences to our polling and we find only 6 different schedules among them.

Here's the breakdown:

Now let's look at how different outcomes can result from different voting methods. (It's interesting to see how various but otherwise "reasonable" methods can yield such diverse results.)

Plurality - Alpha wins

If the party elected its candidate by a simple plurality, nominee Alpha would win with 18 first-place votes, in spite of the fact that Alpha was favored by less than a third of the electorate and was ranked dead last by 37 delegates.

Runoff - Beta wins

If the party decided that a runoff election should be held between the top two contenders, who together received a majority of the first-place votes in the initial ballot, then nominee Beta outranks Alpha for 37 of the 55 delegates and is declared the winner in the runoff.

Eliminate the loser - Gamma wins

If a sequence of ballots were used, eliminating the nominee with the fewest first-place votes at each stage, then the elected candidate would be Gamma.

In this example, the first ballot would eliminate Eta. Of the six delegates voting for Eta in this first ballot, 4 had listed Beta as their second choice, so their 4 votes would go to Beta in the second ballot. The other two "Eta-voters" had Gamma listed as their second choice, so Gamma would pick up their votes on the second ballot. This second ballot would eliminate Delta. Those voting for Delta in the second ballot would then select their runner-ups in the third ballot. On the final ballot, Gamma would win.

Borda count - Delta wins

Since each delegate provided a complete preference schedule, the party might have decided to use a straight Borda count to pick the winner.

Each first-place vote would get 5 points, each second-place vote would get 4, and so on. The highest total score, 191, is then achieved by Delta, who wins. Note that Alpha has the lowest score of 127 and Beta, the second worst, with 152.

Condorcet - Eta wins

Here, each nominee is matched head-to-head with every other.

Eta wins over Alpha by a vote of 37 to 18, over Beta by a vote of 33 to 22, over Gamma by a vote of 36 to 19, and over Delta by a vote of 28 to 27. Eta is the only nominee to beat every other nominee, when paired against only one other nominee at a time.

As you can see, which of the 5 nominees is selected could very well depend on the method you use to tally the results and decide.

Good Can Be Simple

Looking at the above examples and the table of preferences for the delegates, you may notice that Eta is always in the top three ranking positions. Delta is in the top three for all but 10 delegates, too. Alpha, although tops for one group, simply doesn't even show up in the top three ranks for 37 out of 55 delegates and, in fact, is dead last for those 37. This suggests an idea that has also born out well when evaluated by deductions from rigorous decision theory: approval voting.

Approval voting is another method of tallying, which simply allows each voter (or delegate in the above example) to give a vote for each candidate or option on the slate (and withhold that vote, as well.)  No limit is set on the number of candidates/options that an individual can vote for: they can approve of as many choices they like and withhold approval for those they don't. This system replaces the "one person, one vote" with "one candidate, one vote" and the winner is the candidate or option receiving the largest number of approval votes.

Approval voting is an excellent method applied to a wide variety of circumstances. It's robust and yields good, intuitive results with very few exceptions. And it is particularly good in multi-candidate contests such as party primaries and it works well where more than one candidate or option may win; for example, in electing a limited number of new members to an academy or board from a larger group of candidates. (For example, in the case of the 100+ candidates in the recall election in the USA's state of California, where Arnold Schwarzenegger was selected as Governor.)

Approval voting is practical, very easy to explain due to its similarity to existing, common voting methods, and very simple to implement. It's quite easy to let voters punch out a few more holes, if they wish, or mark a few more boxes. The only change is to then permit and accumulate those votes, when tabulating them. Finally, it gives voters greater freedom in expressing themselves without requiring complex ranking schemes.

In a sentence then, approval voting is simple and versatile and it deserves widespread implementation as the preferred method for social choice.

I've personally been involved in processing punch card votes, much like those of fame from the Florida 2000 election scramble in the United States. In fact, I volunteered exactly the same year, but in the primaries, so I had a very recent experience from which to listen to the news from Florida.

Here in Oregon, we also had "hanging chads" and the like. There was no doubt in my mind, in most cases, that such hanging chads actually represented real votes, though. It's pretty clear to most anyone that a punch was made there, even if the chad itself was still barely attached to the card.

But sometimes, a voter would punch the wrong hole and would try and correct it. Some would place some bit of scotch tape on the wrong punch and then repunch the right one. Or, they'd use something like 'white out' or some other kind of paper repair liquid to fix it. Or, lacking such tools at hand, they'd just punch the right one and circle it with a pen and add a written arrow to let you know the one they really wanted. Sometimes, they'd even add a sheet of paper to clarify the issue.

It was extremely rare to see a case where a voter had made two or more punches, none of which appeared to be preferred over the over, for a situation where only one vote was allowed. But it did happen, in my experience, perhaps once in 50,000 votes, or so. Not often. We'd just pass these on and let the automated system ignore the multiple vote, when it got to it.

Sometimes, cards were a complete mess. Too many corrections or else simply unprocessable by the automated system. These were forwarded on to another committee experienced in jointly (none of us operated individually, we always worked in groups of at least four and always from more than one party affiliation) evaluating these cards and reproducing one that could be processed and counted. These committees also documented their decision process for each vote.

I believe the system works fairly well, at the level I saw it. (I do not trust the computer software which tabulates the votes and forwards the accumulations on to other sites for further accumulations, but I'm a programmer so I'm extra suspicious.) I know that there is only a very small opportunity for those of us processing these cards to improperly adjust them, for example. We are being watched by the others enough so that any overt action would be noticed. We are processing the cards quickly, so that any attempt to check out the actual votes on the card and see an opportunity to make a modification and to then stall long enough to do so would be very difficult. It's possible for a skilled individual, but even then their impact would be limited -- they couldn't hope to make a lot of modifications. Only a few where they could sneak them in.

Our groups always had at least four people and there had to be at least one Democrat and one Republican at the table. Everyone got along well, I think. Most of the people I saw at the processing tables were a little older than the population at large, with many folks over 60. If you get a chance to volunteer for this, take it. It's fun and educational, too.

I've no doubt at all that far too much was made of the "hanging chads" in Florida, back in 2000. Some folks made it sound like tens of thousands of votes were in question over this issue and I rather doubt it. There are lots of hanging chads on the cards I processed; in fact, very few cards I saw had none. But there never was any doubt about the vote on them, either. When someone punches a hole, that chad is clearly 'punched' even if it is still attached. And the other chads were clearly 'not punched,' by comparison. There was no reasonable argument otherwise, from what I saw and handled. A big deal was made, I believe, for political gain -- that's all.

Feel free to email me.

Last updated: Friday, January 06, 2006 11:18