Showing posts with label biases. Show all posts
Showing posts with label biases. Show all posts

Monday, May 28, 2012

Video of Kahneman Talk on Knowing along with some Notes.


By Gary Berg-Cross
2002 Nobel Prize-winning psychologist Daniel Kahneman delivered the 12th Annual Sackler Lecture recently. See my earlier Blog on this.  Some interested parties may have missed this talk entitled "Thinking that We Know". You can see a review of the talk as well as a video of the entire thing at the NYT Review. If you don’t have time for that, the following are some notes from the hour lecture which touched on topics from his recent book (“Thinking, Fast and Slow”).

Kahneman started off in a commonsense philosophical manner talking about knowing. To know implies absence of doubt and true belief. But truth is a philosophical concept, and people disagree about what is true. There’s scientific truth that comes from a shared search for agreed and objective truth. This is the central mission of science. But in science just any belief is not part of the conception. It is possible for “true believers “ not to accept science as the way to truth. They argue that since some belief is central to science therefore it is just another religion.

We need to recognize this gap in ideas of knowing.

As a psychologist a starting point for Kahneman was a discussion of what we have learned from Psychology devised laboratory paradigms of reasoning, especially in natural/social environments.
Here he discussed 'dual-process' model of the brain & theories of reasoning . This is the distinction between 2 types of reasoning systems -  ‘System 1’ and ‘System 2’ processes.
System 1 is an older and FAST form of universal cognition shared between animals and humans. It is probably actually not a single system but a set of subsystems that operate with some autonomy. System 1 includes what people call instinctive or intuitive knowing and behaviors. Kahneman and others like to System 1 processes as those that are formed by associate learning ((associative memory is often called instinctive). They are probably the kind produced by neural networks. System 1 processes are characterized as rapid, parallel and automatic in nature and usually only their resulting product becomes consciousness in humans.
System 2 In contrast is a more recent evolutionary development and is often called deliberate. It is slow and sequential in nature, takes effort (cognitive resources). K asks "What is 13 x 27?" System 2 makes use of the central working memory system. This leads to 2 different ideas of rationality. we apprehend the world in two radically opposed ways, employing two fundamentally different modes of thought – fast and slow.

Kahneman’s earliest study was mentioned in the NAS president’s introduction and Karhneman cites it as evidence of System 2 thinking. Pupils dilate when we engage in deliberately thinking. Yes the eyes are the windows into the mind!

While we like to think of ourselves as deliberate thinkers we are often associative thinkers. But to be fast we think that networks of associations need to be activated. These are not necessarily logical and they provide some quick but biased interpretations and are afforded by other associations. This makes for a Blink knowing, but often a deceptive one.
Take an association to the work “bank” in "approach the bank". A quick interpretation might select a meaning by frequency of use. Then "approach the bank" means going towards a financial institution rather than a river bank. It could also be primed by a related word so if we hear “fish” and “bank” then river is a more likely association.
You’ll have to see the video to see how Kahneman woos the audience with his story about his wife’s phrase "sexy man" and what he felt he knew she said afterwards as “doesn't undress the maid himself.”

As shown by studies a
ssociative memory interprets the present in terms of the past. In effect we produces stories that make sense based on these past associations (“sexy and “undress” are related). A good story makes associative sense. And this happens on stock market. It’s not deliberate reasoning but sloppy associative. Stats for atctual analysis of the performance of fund managers over the longer term shows that investors do just as well when basing financial decisions to a monkey throwing darts at a board. There is a tremendously powerful illusion of expertise that sustains managers in their belief their results, when good, are the result of skill. Kahneman explains this as a bias and thus "performance bonuses" are largely awarded for luck or stacking the deck and not real skill at projecting the future.

At this point K started citing studies showing how our interpretations of the likelihood of things is often not logical. What is the overall probability of a flood in California. People say small. Bit if asked the probability of a Flood from an earthquake in CA, the probability is higher, even though the probability of such things such be part of the first probability. Why the illogic? It’s just a better story.

At this point K moved to the topic of what is a valid argument? Truth and validity get confused as shown in the example below”
  • All roses are Flowers
  • Some Flowers fade quickly
· Therefore some Roes fade…..while that seems possible it is not logically true.

This shows that we reason by associations back from conclusion. Correct order is important for valid inference but not associations.

Kahneman provided some examples on the synergy of associations and how the environment influences what we think. If you hold a pencil between your teeth, forcing your mouth into the shape of a smile, you'll find a cartoon funnier than if you hold the pencil pointing forward, by pursing your lips round it in a frown-inducing way you feel more disgust for the cartoon. K had fun with this story. See also Timothy D Wilson’s book Strangers to Ourselves.

Associative coherence and emotion work differently than logical coherence. For emotions that have fit and adhere. This is suggested by a
Paul Rozin’s poison experiment (Rozin et al. 1990). In Rozin’s experiment participants are shown 2 empty bottles that are subsequently filled with sugar. The experimenter then shows the participant two labels, one saying ‘Sugar’, the other saying ‘Sodium Cyanide.’ After reading the labels, participants are more hesitant to drink from the bottle with the ‘Sodium Cyanide’ label even it has OJ in it. There is associaton-based discomfort with.
And associations with particular people works strongly too. What we associate with a person has a great deal with how we believe and how we feel.
Most ideas come from people we like. That is a social belief comes from emotional trust.

K mentioned AmosTversky’s socialcultural theory of attitudes. Social leaders may have attitudes on certain topics for arbitrary historical reason. But as likeable leaders they often can influence many attitudes.

Interactions between System 1 and 2 was a big part of K’s talk.
System 2 is used for control and may follow a series of rules. It partially monitors system 1. How it works is shown by the classic math problem: A bat and a ball together cost $1.10. The bat costs a dollar more than the ball. How much does the ball cost?
Your intuitive system for association may quickly tell you that the ball costs 10 cents. That would be an easy solution, but it would also be incorrect but it is the choice of may even at MIT. Why? We are cognitively lazy. People who delay gratification as shown by a Psych test and have more self control do better on this type of problem. It is more System 1 control.

Scientists should be big System 2. After all they have to pass hostile reviews to get published.

Kahneman says one of his favorite examples of System 1 thinking is what happens when you hear an upper-class British voice say, "I have large tattoos all down my back. People who speak with an upper-class British accent don't have large tattoos down their back. It violates our associative knowledge. So the brain must be bringing vast world knowledge to registers that there is an incongruity here. It happens within three- or four-tenths of a second and it's the same response you'd get if you heard a male voice say, "I believe I am pregnant."

So association makes us ready to respond, but it comes with rigid expectations. An example was hearing that “Julie reads in year 4.
Then you get asked “What's here GPA?” Usually it is high.
It’s as if we have a distribution for each (GPA and reading) which gets mapped together. But there are too many intervening events to accurately predict this.

An example concerns airport insurance. During [the ’90s] when there was terrorist activity in Thailand, people were asked how much they’d pay for a travel-insurance policy that pays $100,000 in case of death for any reason. Others were asked how much they’d pay for a policy that pays $100,000 for death in a terrorist act. Turns out that people will pay more for the second, even though it’s less likely. Why” It’s a policy for an instance of terror vs. dying in general.
We pay more to the terror policy since we fear terror more than death.

this suggests that our associate story telling system 1 is usually in charge.

We like stories and how they sound. If we hear “woes unite foes” it is more persuasive aphorism than “Woes unite enemies.”
A lesson is to communicate to non-experts in a different way. Speak to their story with assoc coherence. This is a lesson for getting the Climate Change story understood. Also the source of the message has to be liked and trusted.
Global warming too distant and abstract so it will take trusted leaders to make the case and do it in associative language. Anecdotes are concrete and specific so they are preferred over facts.

Tuesday, May 22, 2012

Condorcet and Dreams of Reason


By Gary Berg-Cross
 
I’m a big fan of the Enlightenment, its products (Encyclopedia), values (the notion of progress), traditions and influence. I agree with Jürgen Habermas that its ideas along with democratic ideas has the potential for transforming the world and arriving at a more humane, just, and egalitarian society through the realization of the human potential for reason. I agree with Kant, that the Enlightenment marked:
"Mankind's final coming of age, the emancipation of the human consciousness from an immature state of ignorance and error."
But I also agree with Habermas (and others like E.O. Wilson in Consilience ) that the Enlightenment is an "unfinished project." It was a start on emancipated thinking but has not been able to universalize this or remove large islands of ignorance, intolerance and error. It’s successes and shortcomings are something we can learn from. Like Habermas I think that one of its passionate, strategic thrusts, the idea that certainty in moral, social and politics issues will emerge from the application of the scientific method to society, should be corrected and complemented by modern understanding, but not discarded. 
What type of corrections? Well considerations of rationality for one and how it is applied successfully to reform society, understand morals and politics. With the idea of progress comes the idea that morals and politics will become more the products of rationality and greater factual knowledge generated by Science. That’s not exactly what happened in the 19th and 20th century. 
One inspirational starting point and humbling lesson comes from that the great French mathematician, philosopher Revolutionist, and Enlightenment figure Condorcet (1743-1794- full name Marie Jean Antoine Nicolas de Caritat Condorcet). In NNDB, an intelligence aggregator that tracks the activities of people they have determined to be noteworthy, H B Acton described Condorcet as:

Wholly a man of the Enlightenment, an advocate of economic freedom, religious toleration, legal and educational reform, and the abolition of slavery, Condorcet sought to extend the empire of reason to social affairs. Rather than elucidate human behaviour, as had been done thus far, by recourse to either the moral or physical sciences, he sought to explain it by a merger of the two sciences that eventually became transmuted into the discipline of sociology.

He was indeed one of the pioneers in the invention of an analytic, Social Science. He provided the Enlightenment movement some social theory and these remain an important contribution, but his approach did not provide a simple path to Enlightenment goals. Among other things Condorcet struggled to find logical-scientific ways to understand individual and group choice.  One issue was how best (most rationally) conduct voting to advance Democracy. The idea was to apply mathematical principles to social/group decision making and human choice? (Condorcet was a mathematician and well versed in probability which he was eager to apply to social issues. )
So he expected that rational/mathematical analysis could (and would) establish an authoritative system of ethics, aesthetics, and knowledge -something we are still debating and working on. Early on Condorcet argued that through voting, people were more likely to make correct group decisions. But when he modeled voting analytically to check this out he found mathematical paradoxes in it, as did Noble prize winner Ken Arrow many decades later. (In 1972 American economist Kenneth Arrow, together with Sir John Hicks, was awarded the Nobel Prize in economics for work in this area - “pioneering contributions to general equilibrium theory and welfare theory.”) As explained in Wikipedia the voting paradox (also known as Condorcet's paradox) is a situation noted by the Condorcet, in which collective preferences can be cyclic (i.e. not transitive meaning that if A beats B and B beats C then A also beats C - but this isn't what happens in a cycle). Cycles are paradoxical, because they mean that majority wishes can be in conflict with each other. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals. Thus the usual collective democratic decision-making principles don’t generate correct, consistent and stable results. 
Discouraging as was Condorcet personal  participation in the French Revolution.  Part of that story based on brief biographies is culled below:

When the French Revolution broke out Condorcet championed the liberal cause. He was elected as the Paris representative in the Legislative Assembly and he became the secretary of the Assembly. He drew up plans for a state education system which were adopted. By 1792 Condorcet had become one of the leaders of the Republican cause. He joined the moderate Girondists and argued strongly that the King's life should be spared.
When the Girondists fell from favour and the Jacobins, a more radical political group led by Robespierre, took over, Condorcet argued strongly against the new, hurriedly written, constitution which was drawn up to replace the one which he himself had been chiefly responsible for drawing up. This showed a lack of sense and he paid for it when a warrant was issued for his arrest.
Condorcet went into hiding and wrote his very interesting, seminal philosophical work Esquisse d'un tableau historique des progrès de l'esprit humain (1795). Sketch of a Historical Picture of the Progress of the Human Mind . Sketch pretty much descibes all he had time for. It was a sketch outlining what was supposed to be a much larger,full picture work. In March 1794 he thought that the house in which he was hiding in Paris was being watched by his enemies and he no longer felt safe. So he fled from Paris but after 3 days he was arrested and imprisoned. Two days later he was tragicaly found dead in his prison cell of unknown causes. Was he murdered or did he take his own life? His death robbed of much including his plan Historical Picture, which was to be the grand defense of his philosophical system.

As J Herival notes of Condorcet:

... Condorcet was no politician. His uncompromising directness of manner and inability to suffer illogical windbags in silence made him many enemies and few friends. His weak voice, lack of oratorical powers, and tendency to bore the Convention by the excessive height of his arguments was one of the tragedies of the Revolution.
 
Condorcet left us with a martyr to the dream that mankind might directly be freed from error with a simple progressive idea that improves on past belief.  The dream is if only we had processes to get factual information and cogent arguments widely disseminated. Sounds good, but it didn’t work in the emotions of a revolution and now we now understand the problem a bit better. I don't blame a devil , nor do I deem the dreams of reason.  But emotions can override reason, and it happens with some people more than others. Progress can be blocked and the dream of reason deferred. Furthermore, there are probably evolutionary reasons that establish this variability of emotion/reason balance. People who are not as open to the facts are not necessarily stupid or stubborn. Some may be, but others are wired (and acculturated further) to process and react to information differently. As the cognitive linguist George Lakoff put it:
So to attack (that) “belief” through logical or reasoned argument, and thereby expect it to vanish and cease to exist in a brain, is really a rather naive idea. Certainly, it is not the wisest or most effective way of trying to “change brains,”
And changing brains is something needed to advance the Enlightenment vision. One modern interpretation of our dilemma is that rationality and the advancement of knowledge are great values, but they need strategic allies in the Enlightenment effort against institutionalized ignorance that prevent progress.  
For more  on this see my blogs on Confirmatory Bias and for more on Condorcet see Mooney’s "The Republican Brain: The Science of Why They Deny Science -- and Reality."

Monday, May 21, 2012

Thinking that We Know and the Science of Thinking


by Gary Berg-Cross

2002 Nobel Prize-winning psychologist Daniel Kahneman delivers the free 12th Annual Sackler Lecture tonight at 6 at the National Academy of Sciences Building - 2101 Constitution Avenue NW - Auditorium (Washington). The talk is called "Thinking that We Know". Kahneman got the Nobel Prize for research that challenged the rational model of judgment and decision making. Steven Pinker, who I hope is know to this group, called him "one of the most influential psychologists in history and certainly the most important psychologist alive today."

For those who have not read his recent book (“Thinking, Fast and Slow”) the talk should covers some of his ideas on different modes of thinking and the search for the truth. Here is the abstract for the talk:

Truth is a philosophical concept, and the shared search for agreed and objective truth is the central mission of science. But the sense of truth is a subjective experience, which falls in the domain of psychology. Carefu
lly reasoned argument is one way to induce a sense of truth, but it is not the only way, or indeed the most common. The distinction between different modes of thinking – fast and automatic vs. slow and controlled – provides a framework for understanding the variety of experiences of truth.

The New York Times review of
“Thinking, Fast and Slow” noted this:

Human irrationality is Kahneman’s great theme. There are essentially three phases to his career. In the first, he and Tversky did a series of ingenious experiments that revealed twenty or so “cognitive biases” — unconscious errors of reasoning that distort our judgment of the world. Typical of these is the “anchoring effect”: our tendency to be influenced by irrelevant numbers that we happen to be exposed to. (In one experiment, for instance, experienced German judges were inclined to give a shoplifter a longer sentence if they had just rolled a pair of dice loaded to give a high number.) In the second phase, Kahneman and Tversky showed that people making decisions under uncertain conditions do not behave in the way that economic models have traditionally assumed; they do not “maximize utility.” The two then developed an alternative account of decision making, one more faithful to human psychology, which they called “prospect theory.” (It was for this achievement that Kahneman was awarded the Nobel.) In the third phase of his career, mainly after the death of Tversky, Kahneman has delved into “hedonic psychology”: the science of happiness, its nature and its causes. His findings in this area have proved disquieting — and not just because one of the key experiments involved a deliberately prolonged colonoscopy.
“Thinking, Fast and Slow” spans all three of these phases. It is an astonishingly rich book: lucid, profound, full of intellectual surprises and self-help value. It is consistently entertaining and frequently touching, especially when Kahneman is recounting his collaboration with Tversky. (“The pleasure we found in working together made us exceptionally patient; it is much easier to strive for perfection when you are never bored.”) So impressive is its vision of flawed human reason that the New York Times columnist David Brooks recently declared that Kahneman and Tversky’s work “will be remembered hundreds of years from now,” and that it is “a crucial pivot point in the way we see ourselves.” They are, Brooks said, “like the Lewis and Clark of the mind.”

Daniel Kahneman,
P.h.D., is a Senior Scholar and Professor of Psychology and Public Affairs, Emeritus, at Princeton University. His bestselling book, Thinking, Fast and Slow, was selected by The New York Times as one of its Best Books of 2011. A 2002 Nobel Prize winner in economic sciences, Dr. Kahneman has laid the foundation for a new field of research, called behavioral economics.

Sunday, April 03, 2011

Bracketology, Biases in Inexact Sciences, Energy Futures & Religious Projections


Spring in the DC region can be a mixture of both wonderful & maddening things. The cherry blossoms are wonderful. The budget battle is maddening. We are just ending a type of furious wonder with basketball's March Madness. This year with a baker's 68 we have a small extension of madness into April. Someone once describe the tournament as 4 weeks of Super Bowls!

I enjoy it, but do not participate in one thing that adds to some people's entertainment. This is filling out (and gambling on) brackets to predict the winners as the tournament unfolds. After the Sunday announcing the brackets people get their office copy machines busy on Monday. This locks in commitment for the next few weeks. (But another perspective from 1 survey is an estimate that March Madness distraction, during the 1st week of the tournament games are on Tuesday, Thursday and Friday afternoon, could cost employers as much as $1.8 billion in unproductive wages.)


But this year we hear the groans of people with "busted brackets" as we enjoy the heroics of teams like Butler and VCU. Most people's brackets were burned to toast early as top seeds exited and none of # 1 or 2 seeds made the final four. Saturday's national semifinals featured a No. 3 (UConn) beating # 4 (Kentucky), and # 8 (Butler) beating a ultimate underdog # 11 (Virginia Commonwealth) who had to play in from the new first round of 4.

Each year my son-in-law has my daughter and their kids fill in a bracket and he invites me to participate. This seems reasonable since I spend more time watching the BB season than he does. But I've never tried to fill in a bracket, because there are always teams (like VCU, Arizona, Oakland or Morehead State) that I've not seen in competition. I never feel that I know enough or have good bracketology sense to make even a good wager on likely outcomes. I know that lots of what I would do would involve bias rather than real informed decisions.

But like President Obama I might do as well if not better than supposed bracket experts. By the time of the final 4 the President had none of the finalists, but overall he ranked in the 94.9 percentile of ESPN.com's Tournament Challenge which had 5.9 million brackets were filled out. He was well ahead of supposed experts. Premier college basketball analysts for ESPN and self-proclaimed "king of bracketology" Joe Lunardi thought that all four No. 1 seeds would meet in Atlanta. Dick Vitale with 450 points as at the 21.5 percentile and he had seen most, if not all, of the teams play and had time to analyze then. But Vitale and others seems to have lots of confirmatory bias and favor the big guys or teams they see more of. They talk about the big teams all the time - it plays the odds. Once they get the idea that Pitt is a solid team they have trouble seeing their weaknesses. Note, our local noisy spotlight vampire Tony Kornheiser had an even worse score - 420 points or 12.0 percentile. This performance is up there with Wall St financial experts in 2006-2007.

Part of attraction of brackets is that is just fun to out guess the experts. From a fan's perspective, that's one thing that makes the tournament so special. We may avoid expert biases and get some excitement back underdogs.

But getting the brackets exactly right remains a low probability for anyone. Why is this? With some much time and effort spent, some of it from professionals and experts, one wonders why we don't have better predictions. Bracketology is all very humbling, yet it represents the type of thing that we humans do in understanding the world. Each year more there is more TV coverage of teams including special bracket busting games with match-ups previously seen only in the NCAA tournament. ESPN has numerous shows analyzing teams and ex-coaches and players offering insight. We have the stats on dozens of dimensions - 3 point shooting percentages, rebounding, fouling. We can watch the tape just as if we were a coach preparing for a game. Yet this year we have busted brackets galore.


To me it tells us something about the current, in practice limits of human expertise and knowing. Much of human knowing is guided by simplifications and leveraging assumptions and heuristics. To understand a complex topic we apply some simplifying principles such as "talent wins" or "experience wins".
Sure, but these are qualitative and judgmental. What is a significant talent gap? How do we aggregate across positions? We may be a bit more sophisticated and say. "Quality guard play is more important than interior depth."

Or we may balance things this way:

"Poor foul shooting is not usually an Achilles heel for a top-tier team, because talent can overcome that negative." Such things are in Jared Trexler's "99 Things You Wish You Knew Before...Filling Out Your Hoops Bracket." Jared is National College Basketball Columnist at Sports Network, and I'm not exactly sure how he did this year. His early predictions for the East's 2nd Round had 2 errors - George Mason over Villanova, Clemson over West Virginia. He got 3 of 4 right for the East's Sweet 16 teams: Ohio State, Kentucky, Syracuse, North Carolina but like Obama his regional final was all wrong - Ohio State vs. Syracuse. His West regional final? Duke vs. San Diego State - Nope, all wrong.

Vaguely the whole humbling process suggests a degree of caution in dealing with other complex topics some of which have oppositional frames. The Gulf oil gusher was an us against them saga with technology overtaken by natural risk. Opposition, which we artificially structure in games, reflects choice aspects that we simplify things into. Take energy choices. Do we want nuclear or something else? Well there are many other choices including conservation techniques that may not be considered. This is analogous to not making the NCAA selection cut. You are not part of the conversation.

Once selected as a topic, say for nuclear power analysis focuses on strengths such as benefit and risk . You can view it in a competitive (bracket) fashion and ask if you like the odds of nuclear power being a better choice than say coal. Binary choices are simpler. A front-page story (Nuclear power is safest way to make electricity, according to study) by David Brown in April 3, 2011 Washington Post, illusrates comparative risks of nuclear and coal power. In the data reviewed, nuclear power seems like a far lower of a risk to public health than coal generation. Like our brakets there is lots of data to consider, such as mining deaths vs. deaths from radiation etc.

"Compared with nuclear power, coal is responsible for five times as many worker deaths from accidents, 470 times as many deaths due to air pollution among members of the public, and more than 1,000 times as many cases of serious illness, according to a study of the health effects of electricity generation in Europe."

But there are lots of other factors that whiz by without an easy calculus. There is yet no solution to used fuel storage. There are qualitative factors and projections about the health impacts of climate change. But like expert predictions for BB brackets I've very unconvinced that the analysis reported by the Post is adequate. Citizens do have to choose which energy sources they might support, but the interactions with the environment of each energy approach is more like the team contest and equally hard to predict. Linear projections are untrustworthy tools for dynamic situations and there is always the aspect of human biases to wrestle with. It is well known that our perception of risk is not calculated logically from a neutral unbiased view of the evidence. Rather the psychology of how we process a perception and respond to risk situations mixes emotional reactions to how we interpret evidence. We can be very influenced by salient evidence, such as team rankings, the height of players, even their personality. Once we’ve made up our mind about a risk, a confirming bias takes over and we choose to believe the evidence that agrees with what we already believe. All very humbling and cautionary for how we bracket our decisions about important topics.

A final thought on analysis of religions and secular humanist. Don Wharton discussed some ideas on the possible end of religion - http://secularhumanist.blogspot.com/2011/03/end-of-religion.html Again something like a linear projection is involved and cultural paths of rival ideas is likely to be more dynamic. After all the alumni of some groups is pretty strong, has good guard play and a good recruiting system. Of yes, and they can play rough.

It might be fun to think about secularism in a contest with such religions.


We might have the Big Old West religions Christianity: 2.1 billion with many sub-divisions and New East religions Islam: 1.5 billion (all figures from http://www.adherents.com/Religions_By_Adherents.html

In the New West we have :

Secular/Nonreligious/Agnostic/Atheist: 1.1 billion

In the Old East we have:

Hinduism: 900 million
Chinese traditional religion: 394 million and
Buddhism: 376 million

That still leaves space for the mid-majors such as

Primal-indigenous (that old Pagan category?): 300 million
African Traditional & Diasporic: 100 million
Sikhism: 23 million
Juche: 19 million
Spiritism: 15 million
Judaism: 14 million
Baha'i: 7 million
Jainism: 4.2 million
Shinto: 4 million
Cao Dai: 4 million
Zoroastrianism: 2.6 million
Tenrikyo: 2 million
Neo-Paganism: 1 million
Unitarian-Universalism: 800 thousand
Rastafarianism: 600 thousand
Scientology: 500 thousand

I'm not exactly sure how to bracket these, but you know who I am rooting for overall. The thing is that predicting a winner in the next few rounds is hazardous and I'm not going to rely on a simple linear projection.