In peer-review, is it common for a reviewer to be shown and asked to comment on other reviewers' reports? Some months ago, I was asked to review a paper for a computer science conference. I submitted my report about a week before the deadline, and I strongly recommended acceptance subject to a few minor corrections.

Just after the deadline, I was contacted by the programme committee member who originally asked me to review the paper. He sent me another reviewer's report (without a name or other identifying information) and asked for my opinion
of it. The other reviewer had recommended rejection on the grounds that an example in the paper supposedly contradicted the claim of the main theorem. I explained that the other reviewer has misunderstood the example (in fairness, the authors of the paper could have stated it more carefully), and I see that the paper was ultimately accepted.

I have never before seen or been asked to comment on another reviewer's report, but my field is primarily mathematics, where there is often only a single reviewer for a paper, and I have only reviewed a few computer science papers.

So my question is this: in fields where it is usual to have multiple reviewers, is it common to be shown and asked to comment on other reviewers' reports? 

A secondary question would be: if it is not uncommon, does it mainly occur when reviewers take opposing positions on a paper, like in the situation I describe?
I don't know about other fields, but this is a fairly common practice in computer science.  Computer science has a very strong culture of significant publications in conferences, which have significantly different reviewing challenges than journal publications.

The key problem is that conferences typically have a large number of papers that all need to be dealt with by a fixed deadline and with a single iteration of revision.  This generally means that:


You have to cast a wide net for reviewers, and are likely to be trying out a "new" reviewer on several papers at once, rather than iteratively.
People typically commit to reviewing far in advance, when the program committee is formed, and may find themselves with less time than expected and no opportunity to ask for an extra couple of weeks to produce a review.
There is no opportunity for the cycles of dialogue between reviewers and authors that happen during the journal manuscript revision process: generally there is no "major revision" option, just "accept with minor revisions" and "reject."


All of this adds up to getting a collection of reviews with more uneven quality and less chance to work the differences through in dialogue.  Outlier reviews can be problematic: a very low outlier can cause an otherwise good paper to be rejected; a very good outlier can cause the authors of a rightfully rejected paper to feel that they were robbed of a publication.

One of the typical ways to try to deal with this (supported nicely by platforms like EasyChair) is to ask the reviewers to look at each others' reviews and to discuss differences.  This way, when there are major differences of opinion, the more careful and informed participants can influence the others to adjust their opinions, just as happened in your case.  Another mechanism (less commonly practiced, due to time constraints), is to allow the authors to write a rebuttal, which the reviewers are then asked to consider and see whether it leads them to adjust their scores.

There are other, more experimental methods as well---many computer science subfields take their conferences pretty seriously, and are constantly tinkering to try to improve them.