Hello,

Both public administration and political science & international relations are prominent UPSC Mains optional subjects. Both disciplines have a high number of students enrolled, but public administration outnumbers the other in terms of the total number of candidates enrolled.

You should take any of these courses as an IAS optional if you have a background or interest in either of them. Otherwise, if both courses are uninteresting to you, you should look over their syllabuses. Examine the overlap with broad studies for yourself. Also, consider what subjects pique your interest and thrill you the most.

Examine the syllabuses for both optional topics. Examine prior year's optional subject questions.

If you choose optional coaching, find out which topics are offered and the level of instruction offered in your location.

If you're still perplexed, study both subjects for a month, devoting equal attention to each.

Check after a month to see which subject you are most comfortable with.

You may also look at UPSC's success rate for optionals.

Hope it helped