### Anatomy of an Online Debate

The Huffington Post ran a curious online debate a few days ago: Is Yoga a Hindu Practice? Let me state right of the bat that I thought the debate was utterly idiotic given that this question was like asking people to vote if baseball was quintessentially American, if the great pyramids were Egyptian, or if the great wall was built by the Chinese. After all, how the heck does a person debate against a fact? By twisting it into a silly insinuation about ownership. Nevertheless, let's look at the debate results measured by market-share for, against, and neutral to the topic, tracked before and after reading the debate.

If this picture is unclear:
For, against, neutral (baseline) = (65%, 26%, 9%).
For, against, neutral (after reading debate) = (66%, 28%, 6%)
So the net result is that the 3% of the undecided split 1% toward 'for' and 2% toward 'against' after reading the debate.

Warning: If you are a predictive analytics connoisseur or swear by rigorous statistical methods, the rest of the post will be cringe inducing, so read on at your own risk.

Given that we have absolutely no data to use other than this pie chart, I tried to 'quick fit' a plausible Multinomial Logit choice model to these results with the aim of personally understanding how useful this debate really was. Toward this, I defined a utility function u(t) = exp (a0(t) + a1(t)), where:
a0 = baseline contribution for (t = aye, nay, neutral)
a1 = debate contribution
market share (t) = u(t) / (u1 + u2 + u3)

Using the 'before' pie chart, I obtained the following values:

where CONST = a0, and a1 = 0 at this point. Again, note that these are just plausible values and not statistically calibrated likelihood maximizing coefficients based on historical individual observations. Next, merrily using the  'after' pie chart to update the utility function taking the debate into account, I obtained the following values:

where DEBATE = a1 that is used to update the utility function. Note that the results don't really change dramatically.

Based on this plausible MNL model, we observe a positive value for a1 for both the 'for' and 'against' since their market-shares increase after the debate, and a negative value for 'neutral' since the debate forces a good chunk of the few fence sitters to switch. To measure the usefulness of the debate to each group, I looked at the ratio of "what was additionally useful" versus "prior understanding", i.e. the ratio utility_before/utility_after given in the last column. The results indicate that the debate itself was pretty close to useless to the overwhelming majority of the voters, i.e. for the 'aye' people (like me) and on the whole, the debate reinforced what they already knew, yielding a tiny usefulness change of about 0.4%. On the other hand, the debate was relatively more useful to the 'nay' people and it incrementally 'hardened their position' by about 6%. More than a third of the miniscule fence sitters actually took a stance and this debate appealed most to them.

Given that the voter response ('elasticity') for a particular choice-group to an event (debate) in an MNL model also depends on the incremental gain possible from their existing market-share, the degree of movement in market-shares for the three groups are not surprising, although the specific direction of the resultant net shift in market shares does indicate that the debate may have had something to do with it. Of course, one can game such online "changing minds" debates by entirely ignoring the debate and starting with a non-favorite position as the baseline and then simply selecting your most favorite position in the end.

On a side note, almost all the 'Yoga' practiced in the U.S and the west is really Yogasana, whose primary function is to help prep your mind and body for actual Yoga, which in turn has nothing to do with whether you can twist yourself into an exclusive USPO patent-protected double-pretzel or not, and everything to do with open-source inner-sciences that aim to rid a mind of ego, exclusivity, and dogma and reach higher levels of consciousness.