I looked at the internals of the two polls. CBS used a subsample of a large pre-recruited national online sample who agree to be interviewed over the Internet. The sample of “undecideds” included both true undecideds and voters who “lean” toward one candidate or the other. Even if we accept the sampling methodology, one factor renders this group of undecideds unrepresentative of undecided voters in the electorate at large — they were recruited to watch the debate. Left to their own devices many of these people probably would not have watched. So the substantial show of support for Mr. Biden in this sample may not have told us much about how attitudes among undecideds in the electorate may have changed.
As for the CNN/ORC poll, it looks to have a slight Republican bias. 33% of respondents identified as Republicans compared to 31% as Democrats and 34% Independents. They were first interviewed on October 8-10 after the post-debate shift in the polls. Those who said then intended to watch the debate were recruited to watch and be re-interviewed. These recruits had quite a positive view of Paul Ryan before the debate took place with a 58% favorability, compared to 47% for the Vice President. After the debate both candidates saw their favorability ratings rise by three points. So I would say the pro-Ryan result from this poll reflected its sample.
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