Some more data from the US house representative since 1942

The black dots in the figure stands for the election result of US house representatives since 1942. Note that the slope seems to be not so dramatic like the presidential election.

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.

Election as a titration process

Election is similar to a titration process if we choose a suitable coordinate system.

Quantum weirdness

Quantum weirdness is so counterintuitive that to comprehend it is to become not enlightened but confused. As Niels Bohr liked to say, "If someone says that he can think about quantum physics without becoming dizzy, that shows only that he has not understood anything whatever about it."

In Murray Gell-Mann, The Quark and the Jaguar. New York: Freeman, 1994, p. 165. Bohr liked to joke about the difficulty of expressing quantum precepts in ordinary language by telling the following story: "A young rabbinical student went to hear three lectures by a famous rabbi. Afterwards he told his friends: ´The first talk was brilliant, clear and simple. I understood every word. The second was even better, deep and subtle. I didn't understand much, but the rabbi understood all of it. The third was by far the finest, a great and unforgettable experience. I understood nothing and the rabbi didn't understand much either.' "

http://www.stanford.edu/dept/HPS/WritingScience/Ferris.htm