Talk of Labor reinstalling Kevin Rudd as leader has dominated the political conversation over the past few days (again). Would making this move put Labor back in a winning position? Or would a move like this — coming apparently so late in the game, after failed challenges and the challenge-that-wasn’t in March — be seen as desperate, ineffective at best, and even counter-productive?

My own take is that Labor is stuck in the polls — and the electorate is “not listening” to their messages — precisely because Labor’s not been listening to the electorate. We don’t have a long nor deep history of public polling on what follows. But my paraphrase would be: (1) the electorate wasn’t happy with the circumstances of Rudd’s removal in 2010. The reality of the parliamentary system aside, many people believe that prime ministers ought to come and go when “the people decide”, not the party. A similar logic is why “direct election” often trumps other alternatives in polls about the shape of a future Australian republic. (2) On balance, the electorate would prefer that the Labor Party and the nation be led by Rudd rather than Julia Gillard. Labor didn’t give us what we wanted, and we’re responding in kind.

But let’s now look at some of the available evidence a little more systematically. I’ll look at five hypotheses: two I accept, three I don’t.

Hypothesis One: It couldn’t be any worse for Labor if they switched to Rudd.

With Labor’s primary vote share in the low 30s, we’re talking about the “Rusted On”. In political science terms, these are people who identify with Labor, who think of themselves as “Labor” when it comes to politics and who will probably vote Labor come hell or high water. It is thus very hard to see how a change to Rudd could hurt. “The only way is up”, and all that.

Hypothesis Two: I’ve read media speculation that dumping Gillard would alienate women voters and cause Labor’s vote share to fall even further. If we’re down to near-bedrock levels of Labor support then women still supporting Labor are unlikely to switch to a Tony Abbott-led Coalition if Gillard is replaced by Rudd. Gillard falling on her own sword would also mitigate against this kind of possibility, remote as it is in the first place.

Hypothesis Three: It would be better for Labor if they switch to Rudd. We don’t have a regular stream of data on this question. But I can’t recall a single poll finding on this question suggesting that a switch back to Rudd would hurt Labor’s chances.

Last weekend’s release of marginal seat polling by ReachTEL for Fairfax was based on a relatively small sample, just 600 voters spread over six electoral divisions in the eastern states. ReachTEL uses Interactive Voice Response (IVR) or “robo-polling” and seems to have had a short field period and hence so little opportunity for “callbacks” to help reduce non-response bias. So I’m betting that this data has been weighted pretty aggressively to help ensure representativeness, or should have been.

Extrapolating to the national level, ReachTEL estimated an average improvement of 6.7 percentage points for Labor if Rudd replaced Gillard, in two-party preferred terms. That extrapolation — from data that has been subject to considerable weighting — has probably got a large margin of error around it, larger than plus or minus four appearing in media reports of the poll. But I’d still bet that the “Rudd effect” on poll-based estimates of Labor voting intentions is positive, not negative.

A Newspoll from three months ago (8-10 March 2013) yielded the estimates reported in the table below. The apparent gain from a switch to Rudd is a massive 13 points of first preference vote share, from 34 to 47 percentage points, with the Coalition’s first preference vote share falling from 44% (roughly the same as the 2010 election) to 39%. In two-party-preferred terms, the hypothetical Rudd switch apparently generates an 8 percentage point swing to Labor, taking it from 48% TPP to an impossibly large 56% TPP (Labor’s biggest ever TPP win was 53.2% in 1983).

Standard Newspoll vote intention Photograph: Newspoll

Standard Newspoll vote intention item reads “If a Federal Election for the House of Representatives was held today, which one of the following would you vote for?” Respondents reporting “uncommitted” responses are asked “to which one of these do you have a leaning?” Rudd hypothetical wording: “If Mr Kevin Rudd was leader of the Labor Party, and Mr Tony Abbott Leader of the Liberal Party, which one of the following would you vote for?” Party percentages exclude respondents expressing no preference, “don’t know” responses and refusals. n = 1,143 “interviews of voters”, live phone interviews.

There is a lot to quibble with here. The “standard wording” doesn’t reference Tony Abbott or Julia Gillard, but the Rudd hypothetical does. It would be interesting to consider an experiment in which survey respondents are randomly assigned to alternative versions of the vote intention question (standard, Gillard vs Abbott, Rudd vs Abbott), so as to reduce the effects of question-order on any given respondent; note that the Rudd hypothetical item appears to have been asked after the standard item and several other items probing satisfaction with the party leaders etc. We’d also want a large sample to allow us to accurately test the differences across the alternate versions of the items. There are numerous other variations on this design, as our friends from the market research world can attest. And rather than just “marginals”, as the table above reports, it would be terrific to see the full cross-tabulation of responses to the standard wording against responses to Rudd hypothetical wording.

But these really are just quibbles. It is difficult to say that the apparent improvements in Labor vote share here are not real. It is hard to imagine the 13 point improvement in ALP 1st preference voting intentions and the 8 point improvement in ALP TPP reported by Newspoll coming from a world in which the “true effect” of a Rudd switch is zero.

The appropriate conclusion, I think, is that, yes, a switch back to Rudd would unambiguously helps Labor in the polls, and almost surely the election later this year.

Hypothesis Four: “Rudd would guarantee Labor victory”. I think this is extremely dubious and far from certain. We’re going to need a lot more than the evidence in extant public polling to make this kind of conclusion.

Hypothesis Five: Some of Rudd’s support in the polls comes from Coalition supporters who are being “strategic” when asked about a preferred Labor leader. That is, they are “making mischief” (thanks Barrie Cassidy), falsely telling pollsters that they’d be more inclined to support Labor under Rudd than under Gillard, hoping that the poll results themselves will stoke the fires for change, creating the picture of a Labor party in turmoil.

I’m usually dubious about hypotheses that endow survey respondents with these kinds of strategic motivations and insight. Decades of research tell us that most people just aren’t thinking about the game that way when they respond to surveys. And even if they were, why is it obvious that the “strategic” response by a Coalition supporter to the “preferred Labor leader” question would be Rudd and not Gillard?

And above all, when we think about how Coalition supporters respond to survey questions like this, we might have to ask what is making some respondents Coalition supporters in the first place? The Coalition is in the high 40s, first preferences, in many recent polls. Maybe some of these respondents would be be back in the Labor column if Rudd was leader, and maybe that is what they are trying to tell us.