Probably the most important dimension, time, isn't ever included in any of these mathematical evaluations of voting systems.
Strategic voting doesn't just happen once, people apply a strategy over multiple elections and can exert influence before the election even happens. In a two-party system the party in charge knows they'll be punished for egregious transgressions - even by some of their core supporters - leading to opposite policies, whereas in multi-party if one party is caught cheating for instance they know voters will defect to a party with similar policies. The parties also act strategically.
If they want to use a satisfaction model it should be lifetime satisfaction, how well the system represented people overall. This may be basically impossible to model without a complete understanding of human nature, but it matters in the real world; if your country gets overthrown or ultimately makes poor decisions it doesn't matter how satisfied you were with the candidates at one point in time.
Strategic voting doesn't just happen once, people apply a strategy over multiple elections and can exert influence before the election even happens. In a two-party system the party in charge knows they'll be punished for egregious transgressions - even by some of their core supporters - leading to opposite policies, whereas in multi-party if one party is caught cheating for instance they know voters will defect to a party with similar policies. The parties also act strategically.
If they want to use a satisfaction model it should be lifetime satisfaction, how well the system represented people overall. This may be basically impossible to model without a complete understanding of human nature, but it matters in the real world; if your country gets overthrown or ultimately makes poor decisions it doesn't matter how satisfied you were with the candidates at one point in time.