What was Kevin Rudd thinking? Seriously. Why would anyone with an ostensibly insatiable desire for reclaiming the prime ministership let the precarious ambience of uncertainty develop to the extent that it did only to then decline an opportunity to challenge? Well, it turns out that Rudd was simply making the ‘optimal’ strategic choice given the circumstances he found himself in.

The leadership saga, for the most part, pertained to two closely related variables: firstly, whether Rudd would challenge Gillard by standing for the leadership in a caucus vote and, secondly, whether a majority of the 100 members eligible to vote in the Labor caucus would back Rudd in a ballot. The relationship between these is that, as was later confirmed, Rudd would only be comfortable challenging if he had a caucus majority and, additionally, the caucus members would only risk switching allegiances if they thought that Rudd would actually run for the leadership (due to the repercussions of supporting the loser in a ballot).

However, despite these two variables being inextricably linked, it’s important to note that other sources of influence further complicated the respective decision-making processes for both Rudd and caucus members.

Factors that influenced Rudd’s decision

• Caucus support levels; 51 votes were required for a majority. Rudd was, purportedly, reluctant to challenge without a ‘significant’ majority as otherwise he would have ‘split the party down the middle’ thus making governing – even if just for a few months – almost impossible.
  
• His commitment not to ‘challenge’ following the February 2012 leadership ballot. To honour his word a ‘drafting’ would have been required.
• Election chances – why would he want to become leader only to lose an election?
• Retirement plans – would he stay on as opposition leader if he lost an election?
• Potential leadership team – would he be content with Simon Crean as his deputy?
• Timing considerations with the parliament’s sitting schedule, the 2013 budget, opinion polling (a short ‘honeymoon’ period before an election would have been likely) and how long – if at all – he could retain the support of the members of the crossbench in the lower house.

Factors that influenced ALP caucus members’ decisions

• Whether Rudd was actually going to ‘challenge’ or, alternatively, if he would require a ‘drafting’.
  
• Opinion polling and the consequent chances of retaining one’s seat at the election.
• The extent to which other caucus members were switching to Rudd. Since the conclusion of the leadership issue, anyone openly backing the losing candidate is basically forced to resign from any ministerial portfolio they have and to head to the backbench.
• Faith in Julia Gillard after the shambolic media reform attempt.
• Personal standing with Rudd; many dislike his leadership style and refuse to work with him ever again.
• Future ministerial and/or leadership ambitions in conjunction with factional ties. Most of the caucus votes along factional lines at leadership ballots; as a result, factional leaders generally need to switch allegiance first unless a caucus member is willing to switch factions.

Simultaneous game theory analysis

Assuming that the decisions of both Kevin Rudd and ALP caucus members are made simultaneously* and that ALP caucus members act in unison to a significant extent, the following game theory analysis can be applied to logically outline the relationship between Kevin Rudd’s decision of whether to challenge and ALP caucus members’ decisions of whether to back Rudd as leader. Keep in mind, however, that the respective decision-making processes are not entirely dependent on each other; the aforementioned factors would have also had some influence.

Please note that the figures provided are arbitrary and for illustrative purposes only.

As can be seen from the payoffs for each course of action, neither Rudd nor members of the caucus have a dominant strategy whereby they receive the highest payoff regardless of the decision made by the other. In fact, there are two outcomes that are equally optimal (as highlighted).

So, has the concept of game theory failed in this situation? No, not exactly. The ‘optimal’ choice simply becomes the one with the highest payoff given what Rudd and the caucus members think the other is most likely to do.

This is exactly what seemed to ultimately occur. Kevin Rudd and his team determined that he was probably going to fall just short of the 51 votes required for a majority and, consequently, he decided not to challenge.

Things just didn’t go as planned for Rudd

Rudd has since revealed that he was only ever willing to challenge if his team was confident that he had the numbers. ‘I asked them “what are the prospects of us obtaining a significant majority” – their collective response was zero,’ he said following his decision not to contest a ballot.

However, when Simon Crean commenced discussions with the Rudd camp to bring on a leadership spill, the outlook was hopeful. While now disputed between Rudd and Crean, Crean is thought to have at least implied to the Rudd camp that he could bring up to 10 caucus members across. Given that the Rudd team believed that they already had 45 of a required 51 numbers for a majority, a successful nomination for the leadership appeared very possible.

While what ultimately followed is now history. The allegation from Rudd of Crean going rogue with his timing for a press conference advocating Gillard to call a leadership ballot (the Rudd camp wasn’t ready purportedly,) and the failure of Crean to actually deliver any additional numbers are believed to be primary reasons for Rudd’s leadership campaign coming undone.

It is worth noting that Gillard had the upper hand from the start. Her first-mover advantage in being able to call a leadership ballot more easily than Rudd – given his undertaking not to ‘challenge’ – enabled her to call for a ballot upon receiving confirmation from her team that she still had a slim majority. She has also been able to actively campaign to secure caucus votes whilst Rudd couldn’t – or at least wouldn’t – coordinate a push for change in caucus because of his undertaking not to actually ‘challenge’.

Kevin Rudd has now publicly stated that there are “no circumstances” under which he would consider returning to the Labor leadership. In addition to this recent undertaking, it’s very difficult to see how Rudd’s optimal strategy will be to challenge again in the future as virtually every member of the Labor caucus seems disappointed with how things worked out and most – even many who were willing to back Rudd – are now, rationally or irrationally, blaming him. That’s politics.

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*Sequential decisions are possible but unlikely given that ALP caucus members’ votes are not necessarily decided until the actual caucus ballot takes place. Additionally, the application of sequential game theory in this situation, with the potential for the inclusion of additional variables such as Gillard calling a leadership ballot (as opposed to Rudd having to do so and thus breaking his commitment not to officially ‘challenge’), is excessively subjective and consequently largely meaningless.