The majority vote method can be a very powerful technique for combining signals from different forecasting models. Binomial probability gives one a sense of how powerful this can be -- provided that the individual models are truly "independent" of each other. 

Suppose, for example, that you have a number of different forecasting models -- each of which has a 55% probability of success on any given day. If these models are independent of each other, the binomial probability formula suggests that greater numbers will bring greater success.  This is shown in the following chart: 
 

Models Voting	Success Probability of Each	Majority Vote Probability
11	55%	63.3%
21	55%	67.9%
31	55%	71.3%
41	55%	74.1%
51	55%	76.4%
61	55%	78.4%
71	55%	80.2%
81	55%	81.7%
91	55%	83.1%
101	55%	84.4%
111	55%	85.5%
121	55%	86.5%
131	55%	87.5%
141	55%	88.3%
151	55%	89.1%
161	55%	89.9%

To me, this principle argues very strongly for the power of a meta-system that combines inputs from as many diverse models as possible. 

However, one must be careful not to rely too literarily on such a mathematical model.  In the real world, forecasting models are never completely independent of each other -- since all input variables are influenced, to a greater or lessor degree, by the same set of news events and other fundamental factors. In other words, all input variables are mutually interdependent.  To make matters worse, if they are all forecasting the same target, that fact makes them interdependent -- in a statistical sense.  While many forecasting models are very different from each other, I do not believe it will be the case in my lifetime that 89.9% accuracy will be achieved on a consistent basis. 

I do believe, however, that a majority vote based on as many high-quality forecasting systems as possible will have a much higher probability of consistent success than any of the individual models incorporated within it.  It is to that end that I have dedicated this website.  My intention is to eventually connect with a circle of dedicated individuals who are proficient in the use of various forecasting systems; and who are willing, as I am, to pool their best insights, talents, capital and technologies together to create a "SuperSystem." 

This is not a short-term goal.  I am much more concerned with establishing trust and a good working relationship with potential partners -- than I am in turning a fast profit.  Until such a venture comes together, I plan to put much of my best information and insights on this website -- for it seems that this process is helping to accelerating the growth and clarity of my own thinking. 

Each week, the Investors Intelligence financial newsletter (www.investorsintelligence.com) conducts a survey of the recommendations published by 140 different financial newsletter writers.  In the chart below, I have compared their forecasts to the changes in the S&P futures contract.  Their opinions are popularly regarded as a contrarian indicator, and my own analysis confirms that you could do well betting against them. 

The upper chart shows the S&P adjusted contract price since 1/1/1996.  In the middle, the bearish consensus minus the bullish consensus is plotted on a graph.  When bullish sentiment prevails, the braph is below 0. 

The chart at the bottom shows the equity you would earn trading one S&P contract using this contrarian strategy. Notice that the contrarian signal is now positive. 

The next chart is also a measure of professional sentiment.  It is called the "bullish consensus" indicator published by Market Vane (www.marketvane.net).  It is also survey of market advisors.  While, superficially, the methodology appears to be similar to that of the Investors Intelligence report, the actual results are quite different -- as the following chart shows: 

This chart starts in early 1988.  It appears that the advisors surveyed were too skeptical of the market during its slow rise between 1988 and 1994.  Then they began to turn bullish, and issued sound recommendations just about up to the market plunge in the fall of 1998.  One might argue that their anticipation of a bear market in 1998 was fully justified, based on valuations and other criteria.  Nevertheless, they were over a year early in their timing of the market's collapse.  But, subsequently, their bear market recommendations were on target. 

The differences between these two measures of sentiment are actually rather profound.  I suspect that if I were to analyze their respective methodologies more closely the basis for these profound differences could become clear.  However, with regard to the majority vote concept as outlined above, it seems that the sentiments expressed by experts would not pass above the 55% threshold I have, somewhat arbitrarily, established for systems participating in a majority-vote procedure. 

Jeffrey 

BioComp Profit Neural Network S&P 500 Futures Contract "MegaSystem" Forecast: 
Friday's close: down from Thursday's close 
Monday's close: down from Friday's close 

Nirvana OmniTrader Composite Technical Forecast for the S&P 500 Futures Contract: 
Short-term, aggresssive strategy: down 

Volatility Breakout System, Daily, for S&P Futures Contract:  
Buy stop order filled Thursday at 877.00 
Sell limit order for Friday set at 888.50 

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