Is there a source for this claim?
The source is a poll conducted by 'Public Policy Polling':
The poll was conducted on Dec 16th and 17th 2015, partially by phone, partially over the internet. There was a total of 1057 respondents, of which 532 usually vote for the Republicans, of which 34% (about 180) answered the following question with 'Donald Trump':
Given the choices of Jeb Bush, Ben Carson, Chris Christie, Ted Cruz, Carly Fiorina, Jim Gilmore, Lindsey Graham, Mike Huckabee, John Kasich, George Pataki, Rand Paul, Marco Rubio, Rick Santorum, and Donald Trump who would you most like to see as the GOP candidate for President in 2016?
One of the following questions in the poll was:
'Would you support or oppose bombing Agrabah?'
The respondents were given the following alternative answers:
- Support bombing Agrabah
- Oppose bombing Agrabah
- Not sure
Among the Trump supporters, 41% answered 'support bombing Agrabah', 9% answered 'oppose bombing Agrabah' and 51% answered 'not sure'. So, at least at a first glance, it may seem as if 41% of Trump's supporters want to bomb Agrabah.
There are of course several issues with this poll.
As already pointed out, none of the options really reflect the fact that Agrabah is a fictional country. There has been a lot of speculation in the comments, e.g. Ryan writes: 'I think it's worth noting that there's probably a significant number of people "In support of" bombing Agrabah because they realize it's a BS question.'. I am honestly trying to avoid speculations or subjective interpretations when answering questions here, but since Sklivvz asks for more elaboration in his comments and the only possible option to get a definitive answer to 'why did you answer X, Y or Z' would be the unfeasible contact with the respondents, here we go: If I as a respondent had known that Agrabah is a fictional country, the only reasonable answer would IMHO be to oppose bombing. Supporting the bombing is fruitless, since the bombing cannot be conducted and answering 'not sure' does also not really fit my intentions. If I had not known Agrabah, one could of course imagine reasonable opinions fitting the different options:
- Support bombing Agrabah: I support bombing anything sounding kind of Moslem or Arab.
- Oppose bombing Agrabah: I oppose military operations in foreign countries without exceptions.
- Not sure: I don't know Agrabah and I am also not sure if they have done anything worth bombing them for.
Another perhaps more disturbing issue is the margin of error due to the unusually small sample size for the poll. Even if the total number of respondents was 1057 (roundabout 1000 respondents is a common sample size for polls), the sampling error increases significantly when splitting the group into smaller subsets. There are several statistical approaches to estimate the error margin for a poll result, but using a rather common formula M=2*sqrt(P*(1-P)/N) with P being the fraction of respondents (41%) and N being the number of respondents (180) gives a margin of error (M) of about ± 7 percentage points, meaning that the real value probably lies somewhere in the range 34-48%. With even smaller sample sizes, the numbers for the other candidates' supporters have an even larger estimated margin of error.
In addition to these two issues, it is also not a big secret that it is easily possible for polling firms to influence the response by e.g. carefully choosing the wording of the question or answer alternatives or by modifying the context of the question. In this particular case, the Agrabah question follows several other legit questions regarding Moslems, Arabs or Islam and even if I am now just speculating again; it is of course not impossible that PPP here on purpose tries to trick the respondents into some kind of 'anti Moslem/Arab/Islam state' to lure them towards a supporting answer. On the other hand, even if PPP tries to influence the answer, one could of course ask why Trump's supporters are statistically significant more easily tricked to support the bombing of Agrabah (41% ±7pp) than the other Republican voters (23% ±4pp) or the Democrat voters (19% ±3pp).
To summarize: The 41% count is the result of a relatively silly poll question. There are several flaws in the poll, but even considering the expected margins of error due to the small sample sizes, the results of the poll shows that Trump's supporters are significantly more eager to bomb Agrabah than both other Republican or the Democrat voters. The difference between the other Republicans and the Democrats is so small, that it falls within the estimated margin of error.
@Tor-EinarJumbo gives what I think is the correct answer, but I would like to add another that addresses @SebastianRedl's comments.
Here is the complete data from the poll. The question about Agrabah had only three responses: 'support bombing', 'oppose bombing' or 'not sure'. Presumably a response of 'I've never heard of that country.' was filed under 'not sure' (though it's also reasonable to believe that people might oppose bombing of countries they had never heard of, or even countries they knew to be fictional).
The 41% figure given for Trump supporters is of all responses. So the full response list is:
- 41% support
- 9% oppose
- 51% not sure (sic. Rounding errors)
The figures of around 50% 'not sure' is fairly constant across all the Republican primary supports, with the happy exception of George Pataki, whose supporters returned a 100% 'not sure'. Presumably George Pataki scores high among people who listen to questions and know the names of countries.
The 50% 'not sure' is also fairly constant across all other demographics.