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Volume 9: Number 4: Article 1
Decision Augmentation Theory: Applications to the Random Number Generator Database
Edwin C. May, Science Applications International Corporation, 330
Cowper St., Suite 200, Palo Alto, CA 94301
Jessica M. Utts, University of California, Davis, Division
of Statistics, Davis, CA 95616
S. James P. Spottiswoode, Science Applications International
Corporation (Consultant), Menlo Park, CA
Decision Augmentation Theory (DAT) holds that humans integrate information
obtained by anomalous cognition into the usual decision process. The
result is that, to a statistical degree, such decisions are biased toward
volitional outcomes. We summarize our model and show that the domain
over which it is applicable is within a few standard deviations from
chance. We contrast the theory's experimental consequences with those
of models that treat anomalous effects as due to a force. We derive
mathematical expressions for DAT and for force-like models using the
normal distribution. The model's predictions for the random number generator
database are significantly different for force-like versus informational
mechanisms. For large random number generator databases, DAT predicts
a zero slope for a least squares fit to a (Z^2, n) scatter diagram,
where n is the number of bits resulting from a single run and Z
is the resulting Z-score. We find a slope of (1.73±3.19) X 10^-6
(t = 0.543, df = 126, p = 0.295) for the historical
binary random number generator database which strongly suggests that
some informational mechanism is responsible for the anomaly. In a 2-sequence
length analysis of a limited set of data from the Princeton Engineering
Anomalies Research laboratory, we find that a force-like explanation
misses the observed data by 8.6-sigma; however, the observed data is
within 1.1-sigma of the DAT prediction. We also apply DAT to one pseudorandom
number generator study and find that its predicted slope is not significantly
different from the expected value. We provide six circumstantial arguments,
which are based upon experimental outcomes against force-like hypotheses.
Our anomalous cognition research suggests that the quality of the data
is proportional to the total change of Shannon entropy of the target
system. We demonstrate that the change of Shannon entropy of a binary
sequence from chance is independent of sequence length; thus, we suggest
that the change of target entropy may account for successful anomalous
cognition and random number generator experiments.
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