Lee-Yen Wang writes:

I have a question about comparing polls in presidential elections in Taiwan.

The four candidates are:

– Mr. A: Hou Yu-ih, mayor of New Taipei City, from Taiwan’s main opposition Kuomintang (KMT) party.

– Mr. B: Dr. Ko Wen-je, ex-mayor of Taipei, Chairman of the People’s Party (TPP), a much smaller opposition party than the KMT.

– Mr. C: Lai Ching-te, Vice President and the Chairman of the Democratic Progressive Party (DPP), the ruling party.

– Ms. D: Hsiao Bi-khim, former envoy to the United States and a member of the DPP.

My question concers the best method for comparing polls to determine the optimal candidate pairing for president and vice president.

The scenario involves two competing candidates, Mr. A and Mr. B, who want to decide who should be the presidential candidate and who should be the vice presidential candidate, while facing a decided pair, CD.

Polls are conducted for both AB vs. CD and BA vs. CD. Different combinations of AB and BA may have varying strengths against CD. The poll comparisons are listed below, with only the title row representing the comparison shown:

AB CD AB-CD BA CD BA-CD (AB-CD) -(BA-CD)

My question is: which approach is more reasonable for determining which pair of combinations, AB or BA, is stronger against CD?

A and B campaigned heavily for the presidential nomination, with the loser in the polls becoming the vice presidential candidate. However, AB-CD elicits a different response in the polls than BA-CD.

This can be simulated: AB vs. CD is 48% to 46%, while BA vs. CD is 41% to 32%. In the case of AB vs. BA, AB beats BA by 7%. However, if we use the difference of the difference, we get 2% vs. 9%, and the difference of the difference is 7%, favoring BA. These two approaches yield inconsistent results. In a high-stakes election where both candidates campaign intensely, which approach do you suggest is theoretically sound for comparison?

The aforementioned scenario played out vividly in the recent presidential election in Taiwan in January. The controversy over resolving the tie ultimately led to the split of candidates A and B just before the official candidate registration deadline.

They each quickly chose their own vice presidential candidates to run against the CD pair.

The key question is how best to compare the poll results. There are several options:
– Should we simply compare AB vs. BA using the margin of error and ignore the situation to compare the difference of the difference?
– Should we use the margin of error as a metric and apply it to compare the difference of the difference?
– Should we instead use the ratio of estimation and normalize the probability of AB and BA?
– Should we employ the ratio method of estimation and compare the difference of the difference, where we normalize p = (AB – CD)/((AB – CD) + (BA – CD)) and q = 1-p? The question is whether this operation makes sense.

Are there other effective methods for comparing surveys that could solve this dilemma?

I have no idea what’s going on in this story. No idea at all. But I thought some Taiwan experts might be interested, so I’m posting here.