Bashier has encouraged members to go back to the drawing board and re-evaluate their preferences on the second round candidates; not simply reiterate their choices for the first round.
The process of arriving at a consensus is not simple.
Already there has been considerable anger from the African nations that neither of their two candidates made it through to round two.
It's notable that all of the final candidates come from the Asia-Pacific. They will be scrambling hard now to pick up the preferences from the African nations.
The key contest in the second round is expected to be between Groser, Brazil's WTO ambassador Roberto Calvalho de Azevedo (reported as having an edge in diplomatic circles) and Indonesia's former trade minister Mari Pangestu (the sole female candidate left in the race).
Azevedo is expected to cancel out Mexico's Hermino Blanco and South Korea' s Taeho Bark is seen as an outlier.
But these calculations are without the inevitable gaming that takes place behind the scenes.
Groser is a highly experienced practitioner who won wide respect when he chaired the two sets of negotiations at the WTO (rules and agriculture) during his period as New Zealand's ambassador to the organisation.
His cachet in international circles has subsequently grown through the role he has played as New Zealand's Trade Minister and Climate Change Negotiations Minister. While Groser is perceived as having an unparalleled knowledge of the intricacies of the Doha negotiations, WTO watchers claim the fact that he is from a rich or developed nation that has already supplied one WTO head, Mike Moore, counts against him.
But Groser's drawback could turn into an advantage if he makes the final cut, given the strong behind the scenes push now coming from the developed world for the final selection rounds to be merit-based.
Azevedo is seen as a major favourite in Geneva. Against him is the fact he has never been a trade minister and may not have the cachet with "capitals" to cut the necessary deals to finish the Doha round.
His big plus is that there has never been a Latin American running the WTO. But Brazil has thrown significant weight, including the use of Government planes, behind his candidacy.
Pangestu's candidacy shocked the New Zealand team running Groser's campaign when it emerged late in December. When Indonesian Trade Minister Gita Wirjawen visited New Zealand earlier last year, politicians from the Prime Minister down had believed Indonesia would support Groser's candidacy.
But with Indonesia hosting the WTO ministerial conference in December, it is not surprising that a formal candidate of their own was declared.
Pangestu is the only woman left in the ring. She was Indonesia's trade minister from 2004-2011 and has been campaigning hard right round the world.
But not all the 159 WTO member states buy the notion that it is the "developing world's turn" to run the global trade machine.
Canada's International Trade Minister Ed Fast spoke for the developed world when he said Canada supports a merit-based selection process and it was imperative the successful candidate possesses the right long-term vision for the WTO, along with the leadership characteristics, experience, proven record of success and commitment required to realise that vision.
"Canada will support the selection of a candidate who has a demonstrated ability to bridge the very difficult gaps between developed, developing and least-developed countries in the pursuit of successful multilateral trade outcomes."
Canada's open foray will be seen by the developing world as harking back to the days when the "Quad" - the United States, Japan, European Union and Canada - was the major deal-making block in global trade politics.
Their power derived from their respective footprints in international trade. But the emergence of the powerful Bric nations (Brazil, Russia, India and China) during the past decade challenged the cosy first-world alliance.
The US, EU and Japan have yet to declare their hands openly. Around the Geneva traps their open support would be seen as fatal to a candidate's chances.
But their influence will play a behind the scenes role.
Groser was in Beijing at the inaugural New Zealand China Partnership Forum when news leaked that he was among the five candidates to go through to the second round.
The WTO selection panel had notified the four candidates who were culled after round one ahead of the formal confirmation on the five candidates who would go on to the next round. It didn't take long for WTO ambassadors and plugged-in Geneva-based trade journalists to use their deductive powers to get the news out ahead of the formal release.
Groser flew to Geneva last weekend.
Late next week, he should know whether he lives to fight another day during the WTO battle or whether it is over.
