Can IIA survive strategic voting?
by Kevin Venzke [Home]

Are some methods more or less independent of irrelevant alternatives (IIA) when voters use strategies that are dependent on which candidates are nominated? For convenience, we use the same strategies as on the /trunc simulation, i.e. truncation strategies not tailored to any specific election method.

It would certainly seem that a possible outcome of this study would be that, given strategizing voters, a complete mess is made of IIA and no method can claim any advantage over any other. Perhaps under some treatment of strategic behavior this is true, but within the context of this study and its treatment of truncation strategy, it seems that actually a number of outcomes are possible. I invite the reader to draw their own conclusions.

Please see /trunc to understand the basic concepts. Here I will focus on details specific to this page.
Bugfixes and changes: Any changes affecting outcomes will be reported here with dates.
2024-06-01: corrected several ways that randomness could sneak into a user-defined method and hurt its IIA performance.
Cautions: There are three buttons at the top for running trials, and they have hotkeys listed under them. Please note ⚠️ that if you hold down these keys to generate a lot of trials, your browser tab may be unresponsive while the results complete.
Premise: We will start with one scenario and then introduce, at a random position, the Red candidate. When solving both the "before" and "after" scenarios, voters employ some strategy, defined by the options. According to the spirit of IIA (independence of irrelevant alternatives), when we add the Red candidate, the new winner should either be the same as it was before, or it should be Red. The victory shouldn't move between two candidates who aren't Red.
Candidate counts in the options: When you select candidate count, or a fixed number of candidates that each voter ranks, this is based on the "before" scenario, whose candidate list is missing Red. That is why the allowed candidate count range is 3-9 instead of 3-10. This creates a problem that there is no way (using the controls from /trunc) to specify that voters always rank all of the candidates. For this reason, a new option "Voters always rank everyone" has been added.
Random options: Most random options from /trunc have been removed, i.e. those which introduce randomness into voter behavior. Randomness would make it difficult to expect IIA to hold very often. One exception is the option to select frontrunners "Randomly." If you use this, then the randomly selected frontrunners will be the same in both scenarios (with Red or without Red running). This means that Red, upon being introduced, will never be one of the frontrunners. I want to be sure to point out this asymmetry.
Handling of ties: As in /trunc, ties in method outcomes are resolved arbitrarily. However, they are handled consistently between the two scenarios with and without Red. For example, if the initial scenario came down to a coin flip between Blue and Green, and after the introduction of Red we reach the same Blue vs. Green outcome, we need the coin flip to pick the same winner both times. Otherwise, relatively indecisive methods would show a lot more IIA failures simply because the coin flip outcomes would make it seem like things are changing more than they are.
Plots: The concepts here are similar to /trunc (and will be annotated below). The dashed yellow/black circle still indicates frontrunners, but for the initial scenario. When Red is introduced, a slightly larger cyan/gray circle indicates the frontrunners in that election. A triangle is always drawn around the Red candidate, just to make it easier to see where it is.
Method selection: This is the same as /trunc for now except that IFPP and SV are excluded, as those methods only supported three candidates.
Loading scenarios: For now this is not possible, although you can load either the before or after scenario into /trunc to reproduce it there. (Candidate colors will be shifted around, though.)

Method list

Below, the term "approval" always refers to "implicit" approval, meaning a voter ranked some candidate above bottom, above some other candidate.
Methods named with a double asterisk (**) are two-round methods, which in the second round go back to the sincere preferences and assume all voters participate in the second round and vote sincerely. For top-two runoffs this is probably fair, but otherwise it is probably cheating, since strategies are possible but not explored. Interpret with caution.
For performance reasons, a tied outcome in a method is resolved arbitrarily.

Use your own method(s)
See here for examples of what to enter below. Note ⚠️ you could hang or crash your browser here!

    Number of candidates (3-9): 
    Number of voters: 
    Plot height: 



    Distribution options:     even    normal    pull half    push half    triangle    non-spatial    blocs
   charisma dimension
Truncation logic
       Voters rank top X preferences: 
       Voters always rank everyone
  Voters rank above-mean candidates
  Voters rank above midpoint between best and worst
Truncation between two frontrunners: How they are chosen
 Randomly    First preferences    IRV final two    Utility (distance)  
 Copeland    Copeland worst two    Above-mean Approval    Above-midrange Approval  
 Copeland 2nd & 3rd place  Condorcet winner vs. best opposition
 % Threshold generosity between the frontrunners  

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