Election as a titration process (revised)

The basic idea is that the current election based on the new electoral system is very similar to the US presidential election - winner of a state get all the electoral votes of that state. So I expect I can get useful information from the data of US presidential election.

So I define x as

Fraction of electoral votes = electoral votes obtained by republican's presidential candidate /Total electoral votes

and y

for US election as

Fraction of popular votes = popular votes obtained by republican's presidential candidate /Total popular votes

but for Taiwan election as

Fraction of seats = seat obtained by KMT /Total seats

As an example, the US presidential election in 2000, (Bush vs. Gore), we have

Popular votes: 50456002(Repulican) , 50999897 (Democrat)
Electoral votes : 271 (Repulican), 266 (Democrat)
Thus, in this case, I have
x=50456002/(50456002+50999897 )=0.497
y=271/(271+266)=0505

I plot the fraction of electoral votes vs. popular votes using the data of US presidential election since 1932 (blue circles in the figure). The result can be fitted by a hyperbolic function: y=tanh(x). There are fluctuation, of course. That was the reason why G. W. Bush got elected, even though Gore got more popular votes.
Additionally, I have also tried to write this function in the form of Henderson-Hasselbalch equation in order to make a connection to the titration curve most chemists are familiar with.

What surprised me was that data from the Taiwan's past 縣市長 election (red solid squares) and result of current election (單一選區, red solid star) roughly fall on this curve given by the US presidential elections! In the figure, I also drew another curve generated by four data points (triangles) taken from previous 立委選舉. Apparently, the slope of this curve is smaller.

This kind of behavior is very similar to phase transition in natural science. I am not sure whether it is possible to work out a theory for this kind of behavior or not.