So, separate from the issue I already raised (that voting system impacts the number and type of candidates available to vote for), I have some other questions about the assumptions of the simulations.
The system must make many assumptions about how preferences are distributed, determined, co-constraining, influence post-outcome feelings, influence voting, how voting influences post-outcome feelings somewhat independent of preferences, and if and how all of these are moderated by the context of the voting system constraints themselves. The outcome of the system is completely determined by such assumptions. There is nothing magical about computer modeling. The models spit out and can only spit out whatever they were programmed to spit out. The assumptions are inherent in the logical code and equations written by the programmer. They are not themselves science. They are math and computer programming.
To be a viable scientific theory not only must each of these assumptions be grounded in and coherent with existing psychological science, but then its predicted outcomes must be tested against empirical behavioral data. Looking at the pretty graphs spit out by such programs deludes some people (often the non-scientist mathematicians and economist who write them) into thinking they are looking at empirical data that tells us something about the theories. It doesn't. It tells us only about the programmer themselves and what assumptions they made to produce those outcomes.
Lets take a brief look on some of these assumptions.
How are preferences for any given candidate are distributed in the population. Are they "normally" distributed with most people having no preference either way, and few having either a strong like or dislike? Or are that bi-modal, with most people having mod-to-strong like or dislike and few being neutral? Or is the distribution "flat" with all levels of preferences equally represented? Also, is the distribution of preferences the same for all candidates? It is highly plausible that the shapes of the preferences distributions among candidates themselves vary along several dimensions, from uni to bimodality, and centered around a neutral point to highly skewed in either direction, and somewhat flat to extremely peaked with most people sharing a similar perference for that candidate. Which of these sets of assumptions is closer to how preferences are actually distributed for candidates and how might the actual voting system impact the distribution of preferences?
Are the preferences of a particular voter for each candidate set independent from each other rather than co-constraining and correlated?
The simulations linked by Ipetrich suggest independent.
In simulations so far, all preferences have been random and independent".
Most relevant psychology would suggest that preferences for things are not independent because they are not determined by the inherent properties of that thing but by the particular context in which the evaluation is made and relative to other options. In fact, the very concept of a "preference" is inherently relativistic. Also, preferences likely co-constrain each other differently for different voting systems. In a single-vote system, voters have no motive to set relative preferences among all candidates, because all that matters for their voting is which single candidate is their favorite? In a range system, they must put every candidate into a relative rank. Thus, the system itself causally impacts how preferences are set and how the constrain each other.
In addition, what exactly is the algorythm the calculates outcome satisfaction based upon preferences?
Again, one of the links says:
"A voter's happiness with respect to the outcome of an election is equal to the voter's preference for the candidate that won the election."
That implies that only the value of the preference for the candidate who wins is the sole determinant of how voters feel about the outcome.
Like the other assumptions of the simulations, this one seems at best devoid of any basis in psychological science and more likely strongly refuted by much psychological science.
There are many alternatives to that assumption. For example, how much higher is my preference is for the winner relative to the other options? IF I love the winner but despise all others, then I am likely to be much happier with the outcome than if I love the winner but also like-to-love several others?
Again, not only are our preferences determined relativistically, but outcome satisfaction is likely determined by an interaction of the absolute level and relative level of preference for the outcome.
In addition, how does actually voting for a candidate impact outcome satisfaction? IOW, my preference will only partly determine my voting because the voting system constrains who, how and for how many I can vote for. Actions themselves are shown to impact emotion and preferences, not just the other way around. Thus, who I actually vote for is likely to impact outcome satisfaction, somewhat independent from and perhaps complexly interacting with the impact of my preferences on outcome satisfaction.
Again, type of voting system is itself something that likely has a causal impact upon preferences, how they are determined and co-constraining, how they impact outcome satisfaction, and voting actions themselves and thus their impact on satisfaction. Thus, it is likely that a separate set of algorithyms must be created for each type of system, each with psychologically plausible sets of assumptions for that context.
The programs in question do not even count as "simulations" if these various assumptions are not set based upon existing psychological data, which they don't appear to be.
They are predictions about what would happen in the fictional and implausible universe that the programmers have not very creatively imagined.