Ranked Pairs

Ranked Pairs (also Tideman, Nicolaus Tideman after ) is a 1987 developed and electoral voting process in which voters specifying multiple preferences.

If there is a candidate, the voters prefer the pairwise comparison over all others, Ranked Pairs ensures that this candidate wins. Due to this property Ranked Pairs is a Condorcet method by definition. In it Ranked Pairs different from other preferential voting methods such as Borda count and instant runoff voting.

Ranked Pairs dissolves the Condorcet paradox by each of the pair with the lowest number of winning votes ignores the fact in the case of circular reasoning when determining the ranking.

  • 2.1 The situation
  • 2.2 counting
  • 2.3 Order
  • 2.4 Assessing
  • 2.5 Example for the resolution of ambiguities
  • 2.6 Summary

Method

The counting of votes is as follows:

Ranked Pairs can also be used to create a complete ranking of the candidates. For this purpose, first the winner is determined. To determine the runner-up, the first winner will be deleted from the list of candidates and a new winner from among the remaining candidates. To determine the third place, the second winner will be deleted, etc.

Counting of pair comparisons

With the vote count all voters' preferences are taken into account. If a selector, for example, indicating " A> B> C" ( A is better than B, and B is better than C ), then the comparison of A: B in A voice added at A: C is also a voice also express indifference C a voice in B. The voter can (eg, A = B): at A and at B. If a voter no preference for one or more candidates, these candidates will towards others worse, and with each other as equally regarded as.

Subsequently, the majority can be determined. If " Vxy " the number of votes, the higher x classify as y, then wins " x" when Vxy > Vyx; and "y" winning if Vyx > Vxy.

Sorting of the pairs

The winning couples, called " majorities " are then sorted from largest to smallest majority. A majority of x over y comes before a majority of z over w if and only if at least one of the following conditions is met:

An example of

The situation

Let us imagine a vote on the capital of Tennessee. The U.S. state has an east- west distance of over 800 km, but only a north- south length of 170 km. Let's say the candidates for the capital are Memphis ( at the very west end ), Nashville ( in the middle), Chattanooga ( about 200 km southeast of Nashville ), and Knoxville ( far to the east, a good 180 kilometers northeast of Chattanooga ). The population of the catchment areas of these cities is distributed as follows:

  • Memphis ( Shelby County): 826 330
  • Nashville ( Davidson County): 510 784
  • Chattanooga (Hamilton County): 285 536
  • Knoxville ( Knox County): 335 749

Let's say the voters will vote according to their geographical proximity. Suppose also that the population distribution of the remaining Tennessee corresponds to that of the population centers, then one can imagine a vote with the following distribution:

The results would result in the following table:

  • [ A] stands for voters who prefer the candidate who is in column header over that which is in the row heading
  • [B ] indicates voters who prefer the candidate who stands in row heading over that which is in the column heading
  • [ NP ] indicates voters who indicated no preference between the candidates concerned

Counting

First, each pair is listed and the winner determined:

Note that both absolute values ​​and as percentages of the total number of votes can be used; it makes no difference.

Sort

Then the votes are sorted. The vast majority is " Chattanooga Knoxville on "; 83 % of voters prefer Chattanooga. Nashville ( 68%) suggests both Chattanooga and Knoxville, with 68 % over 32 % ( an exact tie, which is actually unlikely with so many voters ). Since Chattanooga > Knoxville, and they are the losers, first vs. Nashville. Knoxville added, and then Nashville vs. Chattanooga.

The couples would be thus grouped as follows:

Set

The pairs are set in order. All those couples that would lead to a circle are omitted:

  • Chattanooga fixed over Knoxville.
  • Nashville set about Knoxville.
  • Nashville set over Chattanooga.
  • Nashville set over Memphis.
  • Chattanooga set over Memphis.
  • Knoxville Memphis on set.

In this case, none of the couples causes a circle. Therefore, each is fixed.

Each " setting " adds the graph showing the relationship between the candidates, another arrow. Thus, the plot looks at the end. ( The arrows go from each of the winner of the pair. )

In this example, Nashville is the winner when Ranked Pairs is used.

Example of the resolution of ambiguities

Let's say there is an ambiguity, for example, a situation with the candidates A, B and C.

  • A> B 68 %
  • B> C 72 %
  • C> A 52%

In this situation, we constitute the majority and start with the biggest.

  • Set fixed B> C
  • Set fixed A> B
  • C> A, we use not fixed, as it would create an ambiguity or a circle.

Therefore, A is the winner.

Summary

In the sample ballot Nashville is the winner. This would also apply to any other Condorcet method.

Using the relative majority and some other method Memphis would have won, because it has the most inhabitants, although Nashville would have won in the pairwise vote without further notice.

Using Instant Runoff Voting Knoxville would have won in this example, although more people prefer to Nashville Knoxville.

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