I have two things.

First, in the revised action table, 'effective influencing action' seems to be used as 'action along the causal path to the solution', which is a departure from the context in which it was introduced:

There are two principal ways to identify the leaders of a group:
1. asking the members to identify which members they
regard as most inﬂuential in directing the group, or
2. asking observers to name the most inﬂuential members,
or to record the frequency of effective inﬂuencing actions.

In summary,

1. "influential in directing the group"
2. "influential members" ... "effective influencing actions"

The introduction of the term implies (to me, at least), that effective influencing actions ought to be used as 'actions effective in altering the course of the group'. I suspect that "effective" as a modifier is just misleadingly simple enough to make this non-obvious. It leaves the question "Effective at what?" in the air, and everyone is free to imagine their own answer, and to assume that we all share one common answer.

Second, I think Arnie was a leader, just not a good leader.

As has been discussed in other threads here, Martha does not exhibit leadership in this scenario -- she exhibits some individual problem-solving skills. And, as has been said in other threads, this can lead to a number of implications about leadership != solution-finding. Whether the article is proposing that she was the leader is unclear to me.

Arnie was initially reported as having the highest number of 'effective influencing actions', and by the group's definition, he was their leader. He influenced the actions of the group the most. But think about some information we have about the scenario:

- he left Martha sitting there alone, being silent
- the rest of the group fell into "agitated discussion"
- no clear progress was made over the hour

I'm going to suggest a possible narrative of "leading" this situation by taking imaginary control of Arnie:

After some initial wildness ("agitated discussion"), it would be apparent that the group needs some direction. Trying to take a rational, rather than authoritative approach, Arnie could suggest that everyone propose some courses of action for the group, and write them on a whiteboard, to aid in systematically choosing one / ruling some out. He may have to snap Martha into participation here to get a suggestion from her. This may set her back in her solution -- unfortunate, but necessary.

Now, all the suggested approaches would be up on a board. It sounds like Martha's would be "let's just think it through very carefully", and the others, apparently, would write "let's talk about it", or at least different enough approaches that they warrant agitated discussion.

Seeing the polarization, Arnie could suggest that everyone work on their own approach for 20 minutes, taking some notes, and then report their progress to the team. At that point, if any approach is clearly winning or losing, the team can refocus their efforts. If not, they'll deal with that then.

Twenty minutes later, three or four different approaches would be partly documented (no matter what, some progress is made), and if Martha made more progress than the others, they can now help her break down the problem space. If it can't be broken down, and she's making good progress, everyone else can now go back to doing other work until she's stuck or finished. Then they can help (e.g. unstick her or check it over).

In this scenario, Martha may have finished 10 minutes later, but: the group would spend less time arguing. They might finish earlier by helping her. If that's impossible, they can get other work done while she finishes. If a different approach was more promising, they'd know. And even if no one were to succeed, they'd have documented their approaches and any progress made on them. Arnie could offer to write it all up on the wiki.

There are likely flaws to my scenario, but my point is this: good leadership is not control of the solving of a problem. It also is rarely steps taken to directly solve a problem. Good leadership is facilitating useful communication and organization, preventing distractions, and removing blockers.

Arnie may have been loud and influential, and he was probably the group's leader, but more important than identifying a leader is identifying good leadership. He was just not a good leader.