In an election with several candidates that goes to a second round in which only the two who got more votes in the first one compete; If in the said second round they make alliances with other candidates that already participated, is it statistically valid to add the results each candidate got with the ones of the other candidates they allied with, and project these will be the results in the second round?
As en example, suppose we have candidates $A$, $B$, $C$, $D$, $E$. In the first round
$A$ gets $12\%$
$B$ gets $25\%$
$C$ gets $45\%$
D gets $10\%$
E gets $8\%$
So $C$ and $B$ get to the second round.
$C$ allies with $D$
$B$ allies with $A$ and $E$.
So, is it statistically valid to say that the projection for the second round is?
$C$ gets $(45+10)$ percent = $55\%$
$B$ gets $(25+12+8)$ percent = $45\%$
The core question is ¿what is the valid way to "add" in statistics different percentages, in a "scenario" like this one? ¿or do I have make a whole new model for the second round?
I will add the tag "soft question" because statistics is not my field of expertise, and even though I've tried to google for this, nothing has showed up, but I'm pretty sure it's a really basic question.
Thanks in advance
It is only valid if you assume that the preference of people who voted for C align with those who voted for D. Likewise the preferences for those who voted for B align with those who voted for A and E. Let us make the assumption that everyone has to vote AND that everyone who voted for D votes for C AND everyone who voted for A and E votes for B.Then, and only then can we assume the projection you have given.
For a counter example, imagine 50% of people who voted for D, don't like C. But everyone who likes A and E likes B and in the second round votes for B.If and only if they all have to vote, 50% of the people who originally voted D will vote for C in the second round whilst the other 50% (by our assumption they are forced to vote) will vote B. So C gets 45+5=50% and B gets 25+12+8+5=50%. Suppose now that people who voted for A were don't necessarily have to vote. In this case the 50% who don't like C will abstain from voting. Now C gets (45+5)/(100-5)=9/19 since we are missing 5 and likewise B gets (25+12+8)/(100-5)=8/19.
Let us also take the extreme case where everyone from A and E go against B because for example they do not like B. Let say they have to vote, and they vote for C. Now we C gets 45+10+12+8=75% while D gets a 25% a large change.
You do not need to change the model, simply taken into account your assumptions about which was people's preferences are. If they align exactly with the way the party chooses to ally, then your model is fine. If there are people who do not agree with how 2 candidates ally they may change their preferences and you simply take that into account :)
Let me know if I can clarify!