Dear all, This is a question (more) related to the concept of propensity score matching (PSM). The following description takes from the last paragraph of page 210 of the interesting book "Propensity score analysis: Statistical methods and applications (https://www.stata.com/bookstore/prop...core-analysis/)" (2nd Edition, by Shenyang Y. Guo and Mark W. Fraser):
(Note that, please ssc install psmatch2)
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A few cautionary statements about running psmatch2 are worth mentioning.

When one treated case is found, several nontreated cases—each of which has the same value of propensity score—may be tied.

In a 1-to-1 match, identifying which of the tied cases was the matched case depends on the order of the data.
I agree so far. However, they go on:
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Thus, it is important to first create a random variable and then sort data using this variable.
which I do not agree (I really don’t think that the last step is necessary). In particular, they suggest to do something like this：
Code:
set seed 10101
gen ranorder=runiform()
sort ranorder
before one does the following
Code:
psmatch2 treated x1 x2 ..., common n(1)
My argument is: Suppose that one treated observation T with propensity score (PS=0.8) is matched to three (tied) control observations (C1, C2, and C3, in that raw ordering, all with PS=0.8 as well). If we do not randomly sort again, C1 will be picked up in the 1:1 matching. Suppose that, following your suggestion, we generate random number and sort the raw data according to that number, and now assume that C3 is picked up. Since C1, C2, and C3 are equally good (all with PS=0.8) in nature, and the raw order is also a realization of the population, I don’t see why another realization C3 will be better than the one (C1) without sorting.

I really appreciate any comments from all of you. Thanks!

BTY, Does anyone know that whether the Stata teffects psmatch command does this kind of random sorting before matching (with option nn(1))?