Speaking at a private dinner hosted by PwC on the topic of leadership and values in a volatile world, the questions put to me were “what leadership traits will be paramount in the future?” and “what are the new expectations the public has for business leaders?”

On reflection, it struck me that the conversation this year was very different than in years past. We were no longer talking about reinventing leadership but about adding new elements to the old model.  An additive operation in the algebra of change, as my colleague Stuart Albert would put it, not a subtractive or transformative process.

On the opening morning at Davos, I attended a session entitled “The New Context for Leadership.”  Up for discussion were purpose-driven leadership, collaborating across organizational boundaries and inspiring the younger generation. Peter Grauer, the Chairman of Bloomberg, talked about the results of a study to identify what leadership competencies were most valued in his company.  The top performers had contradictory attributes, what he called the “and factor:” They had future vision but were tactically strong, they provided strong guidance but were open to challenge, they relied on extensive networks but were also capable of moving fast (i.e., unilaterally), they were hands-on but also empowering.

A similar idea was advanced at the Women Leader’s dinner on Friday night, Michelle Bachelet, the former Chilean president said that in changing times the best leaders are those who can be generals one day and consensus-builders the next.  Josette Sheeran, UN World Food Program Executive Director agreed stating that today’s leadership still needs to be hierarchical but also needs to be flexible.

Since the 2008 economic crisis, two very different “rhetoric” about leadership have co-existed. One, the traditional rhetoric, says that our perpetually shifting environment calls for leadership that is more decisive and crisis-oriented than the slow and consensual style that we might prefer in more munificent times. The second, more “politically correct” rhetoric says that the old, command and control model is responsible for many of the problems of the recent years and that only with a more collaborative and inclusive leadership will we get the flexibility, innovation and new thinking that we need to prosper in a fast-changing and hyper-connected world.

Now it seems that we have settled on a solution, not “either or” but “yes and.”

Like Janus, the Greek god depicted as a man with two heads, each facing in opposite directions, our new leader can and must have it both ways: command and collaborate.

There is obvious practical benefit to this kind ambidexterity. But, does it exist and does it inspire? Or is it just a theoretical model?  The people who come to mind when I ask my students about a leader they admire fit the “command rhetoric” (e.g., Steve Jobs) or the “collaborate rhetoric” (e.g., Gandhi), but not both.  Never in 23 years of teaching MBA and executive I have heard someone cited because of his or her capacity to “code-switch” their leadership style.

In fact, when we see leaders who do this effectively we question their authenticity.

But, my questions are not rhetorical for these are clearly complex and volatile times. Are we looking for leaders who can supplement the traditional tool kit or do we want leaders who will transform it?