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Instant Pairwise Elimination (IPE) Elections Give Us Fairness And Better Candidates

We, the voters, are frustrated! The politicians who win elections are always special-interest puppets. Yet we want problem-solving leaders!

Instead of politicians who undermine the economy with corruption, we want leaders who will reduce corruption and dramatically energize the stagnant economy. Instead of politicians who trash the planet, we want leaders who will solve the energy crisis and stop climate change. Instead of politicians who suggest prayer when there is yet another mass shooting, we want leaders who aren't afraid to fight the NRA.

Fortunately we now have a way to cut the puppet strings that connect elected politicians to their biggest campaign contributors. The place to start is by understanding the secret that gives money more influence than votes.

Vote Splitting Secret

The secret link between politicians and their biggest campaign contributors is a divide-and-conquer tactic called vote splitting. Let's see how vote splitting works, and how greedy business owners exploit it using money.

It's rare for a problem-solving leader to enter a U.S. primary election, either in a Republican primary or a Democratic primary. But if such a candidate does enter a primary election, then money is quietly given to yet another candidate who appears to be similar to the problem-solving candidate. The result is that the two problem-solving candidates split the votes of voters who want either one of those candidates. If instead, just one reasonably popular, problem-solving candidate entered the race, he or she would easly defeat the money-backed puppet candidate.

Another secret is that if a problem-solving candidate does enter the race, the biggest campaign contributors use back-room meetings to choose a single money-backed, special-interest puppet. This tactic concentrates all the remaining votes so that they are not split.

Vote splitting reduces the number of votes needed for the special-interest puppet to win. That's because the vote-counting rules do not require the winner to get more than half the votes. The winner only needs more votes than either one of the problem-solving candidates. The splitting of votes between the similar problem-solving candidates reduces how many votes the special-interest puppet needs to win.

In addition, the puppet candidate can afford to buy much more advertising. As a bonus, the people who own newspapers and TV stations (“the media”) are biased in favor of puppet candidates because they buy more advertising than problem-solving candidates.

The only reason this strategy works is because we, the voters, can only mark on our ballot just one of those candidates as our “favorite.” In other words, our secondary preference for the other problem-solving candidate is ignored.

Pairwise Elimination

A much fairer way to count ballots is to use pairwise counting. This pairwise approach is used in team sports where each game is a contest between just two teams. If all the teams were to play against every other team, one pair at a time, a team that lost all its games would clearly be the worst team.

In voting it's easy to do pairwise comparisons between candidates. Or rather it would be easy if we, the voters, were allowed to rank all the candidates. This means that after you mark the ballot for your first, favorite choice, you would mark a second-favorite choice, which would be the second problem-solving candidate. Of course you would mark the puppet candidate as your least-favorite choice, or you could leave their oval unmarked (to indicate your lack of support).

Using ranked-choice ballots, a voter can rank all the candidates using up to 7 ranking levels. (Of course if there are only 3 or 4 candidates in a race, then only 3 or 4 ranking levels are needed.) If a paper ballot is used and space is limited, then 5 ranking levels can be used, even if there are many candidates. It's important that a paper ballot use ovals that are marked or not marked, because asking voters to write a number for each candidate is not reasonable.

RIPE sample ballot

With all this extra information it's easy to identify — and eliminate — the candidate who loses all their pairwise contests with other candidates. And consider that (unlike sports contests), this pairwise-elimination process can be repeated on a computer so fast that the results are available instantly. This process is called “instant-pairwise-elimination,” and it's abbreviated as IPE.

IPE Example

Let's look at an example of instant-pairwise-elimination (IPE) vote counting.

In this example there are 10 voters. Instead of using candidates as the choices being voted on, let's avoid emotional political associations by using four flavors of ice-cream: chocolate, vanilla, strawberry, and mint chocolate chip

The graphic below shows 10 stack of disks. Each stack represents one ballot. Each disk is colored and labeled to represents an ice-cream flavor. The top disk indicates the voter's first choice, the next-to-top disk indicates the voter's second choice, the next-to-bottom disk indicates the voter's third choice, and the bottom disk indicates the voter's last — least-favorite — choice.

ice-cream flavor ballots

Our current vote-conting method is to ignore all the voter preferences except for the first preference.

ice-cream flavor ballots

Notice that vanilla has the most first-choice votes, so our current — unfair — vote-counting rule identifies it, vanilla, as the winner.

But unlike governmental elections, here we have all the preferences. So we can look deeper into the voter preferences. To do that we use pairwise counting.

Comparing chocolate to strawberry reveals that chocolate loses its pairwise contest against strawberry. That's because 6 voters prefer strawberry over chocolate, but fewer voters, only 4, prefer the opposite, namely chocolate over strawberry.

ice-cream flavor ballots

Next we see that chocolate loses its pairwise contest against vanilla because 6 voters prefer vanilla and 4 voters prefer chocolate.

ice-cream flavor ballots

Looking at the other pairwise contest that involves chocolate, we see that chocolate loses its pairwise contest against mint chocolate chip. In this case 7 voters prefer mint chocolate chip and 3 voters prefer chocolate.

ice-cream flavor ballots

Chocolate looses all three of the pairwise contests it's involved in, so it's elminated as the “pairwise loser.” That leaves strawberry, vanilla, and mint chocolate chip. (There can't be a second pairwise loser in the same round because chocolate was compared to every other flavor.)

Next we look at the pairwise contest for vanilla and strawberry. Vanilla loses because 6 voters prefer strawberry and 4 voters prefer vanilla.

ice-cream flavor ballots

Looking at the other pairwise contest that involves vanilla, We see that vanilla loses because 6 voters prefer mint chocolate chip and 4 voters prefer vanilla.

ice-cream flavor ballots

Vanilla looses both of the pairwise contests that involve the remaining flavors, so it's elminated as the next pairwise loser.

The only remaining flavors are strawberry and mint chocolate chip. With only two flavors remaining, there is only one pairwise contest.

We see that strawberry loses this pairwise contest. Specifically, 7 voters prefer mint chocolate chip and 3 voters prefer strawberry. So strawberry is eliminated, and only mint chocolate chip remains.

ice-cream flavor ballots

This means mint chocolate chip is the most popular flavor among these voters. So mint chocolate chip is declared the overall winner.

This result fits with what we see in the original ballots. The voters do not agree on which flavor is their first choice, but it's obvious that mint chocolate chip is every voter's second-favorite choice.

If this were a political contest, this situation would be like having three extremist political candidates (such as pro-big-business, pro-worker, and pro-small-business), yet all agreeing that a problem-solving leader would be the best second choice.

In case you're familiar with a vote-counting method called “instant-runoff voting” (IRV), notice that it eliminates mint chocolate chip in the first round because it has no first-choice votes. In the second round both chocolate and strawberry have the fewest top marks, so we would peek ahead and see that chocolate deserves to be eliminated next. In the third round strawberry would win against vanilla. Here the IRV winner, strawberry, is more realistic than the traditional first-choice-only-counting winner, vanilla, but IRV fails to look deeper into the voter preferences, so it fails to correctly identify the most popular choice.

ice-cream flavor ballots

Now you understand the instant pairwise elimination method. It repeatedly eliminates pairwise losers until only one choice remains.

Rock-Paper-Scissors Cycles

Sometimes this pairwise-elimination process reaches a point where there isn't a candidate who loses all his pairwise contests. How is this situation resolved?

At this point we, or a computer, can look at all the ballots and ignore the names of candidates who already were eliminated. And on each ballot we can identify which remaining candidate is now at the “bottom” of the voter's ranking. The candidate who is at the bottom of the most ballots becomes the next candidate to be eliminated.

In case you care, this bottom-elimination rule is basically an upside-down version of instant-runoff voting.

General Elections

So far we have a method that identifies the most popular candidate as the last remaining candidate after repeating the instant-pairwise-elimination process. If this counting is done in all the primary elections — especially the Republican and Democratic primaries — then the general election will be a contest between a Republican problem-solving candidate and a Democratic problem-solving candidate and one or more third-party problem-solving candidates.

Take a moment to appreciate the pleasant feeling of being able to enthusiastically mark your ballot for a candidate you really like. Until then, as long as we continue to use our primitive single-mark ballots, we have to “hold our nose” as we mark the lessor of two evils.

Also appreciate that if you don't like either the Republican candidate or the Democratic candidate, you can mark a third-party candidate as your first choice. And then you can mark either the Republican candidate or the Democratic candidate as your second choice. Very importantly, your first-choice vote for a third-party candidate will not be wasted because instant pairwise elimination allows for the possibility that either the Republican or Democratic candidate is eliminated first, so that your third-party favorite has a chance of winning against the remaining big-party candidate.

U.S. Presidential Elections

Everyone likes to talk about the unfair way in which U.S. Presidents are elected. Especially the issue of the electoral college. But resolving that unfairness requires a first step of voters gaining experience marking ranked ballots.

Instant pairwise elimination (IPE) counting is not an appropriate choice for presidential elections. Why? Because looking at ballots to deal with rock-paper-scissors-like cycles isn't practical. Fortunately there are vote-counting methods that are just as fair as IPE (and possibly fairer), and which only involve looking at pairwise counts, which are easy to collect and easy to combine.

At that point it will be easy to re-define electoral votes as decimal numbers. This simple change eliminates the electoral college, but without eliminating electoral votes.

Why are electoral votes still needed? They protect states with bad weather on election day from being out-voted by states having good weather on election day. And they protect less-corrupt states from corrupt states that use discriminatory polling-place line lengths to bias voting in favor of the political party that controls that state's legislature. And electoral votes protect voters in polling-place states from states that use mail-in ballots.

Getting to those fairer presidential elections requires that, first, we need to adopt fairer ballots and fairer vote-counting methods at the state level.

Centrists versus extremists?

Some people argue about whether a “centrist” candidate should win instead of whichever candidate is most popular. But that concern overlooks the fact that the job of a governor or mayor is to enforce laws. Those laws are created by the state legislature and city councils. So if the elected official becomes biased, or corrupt, and acts against the best interests of the voters, then a fully representative legislature or city council can pass a new law that imposes a financial penalty, or a tax, or a jail sentence on anyone who is found guilty of the biased or corrupt behavior.

The reason this balance of power tends to be forgotten is that U.S. Congress and some state legislatures have become so dysfunctional that governors and courts have taken over the role of making meaningful decisions. But this shifting of power away from Congress and state legislatures will shift back when those institutions are filled with problem-solving leaders instead of special-interest puppets. In particular, when Congress is filled with problem-solving leaders, Congress can pass laws that set limits when the U.S. President fails to act in the best interests of most U.S. citizens.

Until this reform occurs, the puppet masters — who are the people who give the biggest campaign contributions — can rather easily pass the corrupt laws they want. And they can continue to block the solutions that most voters want.

It's also worth remembering that stalemate issues involving religion and ethics serve to distract attention away from the lack of progress on laws that the majority of voters want.

IPE Advantages

In summary, instant pairwise elimination provides these significant advantages:

  • It's easy to understand.
  • It gives much fairer results compared to instant-runoff voting (IRV, sometimes misleadingly called “Ranked Choice” voting), approval voting, score voting, STAR voting, and other easy-to-understand voting methods.
  • Compared to many voting methods (such as approval, score, STAR, and IRV) it is not vulnerable to tactical/strategic voting.
  • When there are more than about 200 voters, the results are almost always the same as VoteFair popularity ranking and other Condorcet-compliant methods.

To appreciate how easy it is to understand, here's a full description of the IPE method: “Voters rank the candidates using as many ranking levels as there are candidates. or at least 5 ranking levels if ovals are marked on a paper ballot and space is limited and lots of the candidates are unlikely to win.  During counting, each elimination round eliminates the candidate who loses every pairwise contest against every other remaining candidate.  If an elimination round has no pairwise-losing candidate then, for that round, each ballot gives one count to the lowest-ranked remaining candidate on that ballot, and the candidate with the highest such count is eliminated.  The last remaining candidate wins.”


When an election involves filling multiple seats, such as in a legislature, parliament, or city council, the IPE method can be extended into the RIPE — representative instant pairwise elimination — method.

The RIPE method is a “proportional” voting method. Specifically it awards a second legislative seat to the candidate who best represents the voters who are not well-represented by the first-seat winner. Additionally, the RIPE method reserves some extra “statewide” seats for candidates from smaller political parties who otherwise do not win a fair numbers of district-specific seats.

Please Share

It's time to adopt fairer vote-counting methods at the city and state level. The time is ripe for IPE elections!

Please bookmark this page and share it with friends, coworkers, relatives, and anyone else who is frustrated that elections don't give fully representative results.


Instant pairwise elimination (IPE) was first proposed in 2019 January on the r/EndFPTP subreddit by Richard Fobes, the designer of VoteFair ranking.  It was created as a single-seat-winner method that is easier to understand than VoteFair popularity ranking, and much fairer than IRV (instant-runoff voting).




Cover of Ending The Hidden Unfairness In U.S. Elections Cover of The Creative Problem Solver's Toolbox VoteFair ranking was invented by Richard Fobes who is the author of Ending The Hidden Unfairness In U.S. Elections and The Creative Problem Solver's Toolbox.   Sales of these two books help to make VoteFair ranking available for free at this website.



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