Labor and the Coalition continue to poll in the neighbourhood of 50-50, two-party preferred. The 2013 election is shaping up as a genuinely close affair.

Does the Coalition have to consider the unthinkable? Does Malcolm Turnbull offer them a better chance at victory against a resurgent, Rudd-led, Labor party? The betting markets are certainly toying with the idea. Turnbull’s price in the Liberal leader markets was in to the $4.5 to $6 range this week, after spending the last few months at $7 to $8 or higher. Tony Abbott, of course, remains the firm favourite to lead the Coalition to the election, although the probability of this event implied by the betting prices has fallen to the 69% to 76% range in recent days.

What’s going on? And could, or should, the Coalition be thinking the unthinkable?

In the last Newspoll with Julia Gillard as prime minister (fielded 21 to 23 June, 2013), Abbott led Gillard as “better prime minister”, 45% to 33%. Gillard had been close to level-pegging with Abbott on this measure as recently as April, 2013 and even outperformed Abbott by 10 to 12 points in the last quarter of 2012. Prior to April-June of this year, Abbott had occasionally beaten Gillard on this measure, but never by much nor for long, even when Labor’s voting intention numbers trailed the Coalition’s by large margins.

In the two Newspolls since his return to the leadership, Rudd has dominated Abbott on the “better prime minister” measure: 49% to 35% (June 28-30) and 53% to 31% (July 5-7), or Rudd +14 and +21. The last Nielsen poll (July 11-13) yielded 55% to 41% (Rudd +14). We get a similar result from Essential Media’s last online poll: 50% to 35% (Rudd +15). It is also worth pointing out that in the five Newspolls prior to Gillard replacing Rudd (April to June, 2010), Rudd outperformed Abbott on the “better prime minister” measure by margins ranging from +9 to +27.

The conjecture then is that when Gillard presided over a minority government Abbott was an effective opposition leader, but that opposite Rudd Abbott isn’t the Coalition’s best choice for leader – and that maybe Turnbull is.

I’ve couched the discussion above in terms of “popularity”, since “better” can mean different things to different people. But there may be more substance to the “better prime minister” comparisons than mere “popularity”.

For instance, one of the more celebrated theorems in political science is the Median Voter Theorem (MVT). Here’s a non-technical explanation: Assume a majority-rule election with two candidates and an odd number of voters who may not abstain. Each voter has a preferred policy outcome (sometimes called an “ideal point”), represented as a point on a continuum (usually, but not necessarily, considered to be a left-right or ideological dimension). Candidates know voters’ preferences and offer proposals to the electorate. Subject to random errors, voters vote for the candidate whose proposal is closest to their ideal point. The MVT states that under these conditions the two candidates offer the same policy proposal, the preferred policy of “the median voter”, the voter whose ideal point is at the middle of the distribution of voter ideal points.

The MVT helps rationalise why two-party electoral systems often generate policy convergence rather than policy divergence between the parties. Australia’s system of compulsory turnout and preferential voting ensures a rough correspondence between the highly stylised conditions of the MVT and Australian electoral politics.

My hypothesis is that Rudd isn’t just “more popular” than Abbott or Gillard. Centrist voters, following the MVT, see Rudd as “closer” to them than Abbott or Gillard. In the choice between a Gillard-led Labor party and an Abbott-led Coalition, it is as if the median voter preferred the latter. Rudd’s leadership and policy changes represent a step towards the median voter. Much of what we’re seeing in the polls right now – Labor’s resurgence on voting intentions, Rudd leading Abbott on the “better PM” measure – is consistent with this story.

Is Turnbull closer to the median voter than Tony Abbott? And, critically, if Turnbull is, does the median voter know it? Turnbull’s popularity numbers suggest that they do. To take just one example, a Nielsen poll from June 2013 found 62% of voters would prefer him as opposition leader, versus 32% for Abbott.

A 2008 survey I conducted for the University of Sydney’s United States Studies Centre provides some additional evidence. Respondents were asked to place the political parties and leaders on a five-point “left-right” scale; Rudd and Turnbull were leaders of their parties at the time. The results are instructive. The average placements were: Kevin Rudd 2.8, the ALP 2.9, Malcolm Turnbull 3.2 and the Liberal Party 3.4. That is, at least back in 2008, Turnbull was seen as (rather unambiguously) more moderate than his party. Note also that Rudd (2.8) and Turnbull (3.2) were equidistant from the fixed “moderate” midpoint of “3” on the one to five scale provided to respondents. I doubt a survey today would find particularly different results and, moreover, would see respondents tending to rank Gillard, Rudd, Turnbull, Abbott in that order, from left to right.

All this is to say that the “popularity” numbers may reflect a deeper and more substantive truth. Median voters decide elections in two-party electoral systems. In reinstalling Rudd as prime minister, Labor has taken a step to the middle, or is perceived to have done so. Maybe the Coalition will have to think about doing the same.