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<p>Thank you all for the reply's!</p>
<p>To be a little more concrete: ACT-R behaves not as i expected.
The ACT-R documentation gives the following formula
(newutility.pdf, page 2):</p>
<p>P_i = e^( U_i/s ) / \sum_j e^( U_j/s )</p>
<p>which describes the probability P_i that the production i is
chosen in dependence of the s value and all utility values (the
U_j values).</p>
<p>Now suppose that s=1 and we have only two productions. We want to
examine how the utility values U_1 and U_2 have to be chosen so
that P_1=0.6 and P_2=0.4.</p>
<p>By that we have 0.6=e^U_1 / (e^U_1+e^U_2) and 0.4=e^U_2 /
(e^U_1+e^U_2) .<br>
</p>
<p>We can easily derive e^U_1=e^U_2 * (0.6/0.6) and therefore
U_1=log ( e^U_2 * (0.6/0.4))<br>
</p>
<p>So by set U_2=10 we get U_1=10.41... (see
<a class="moz-txt-link-freetext" href="https://www.wolframalpha.com/input/?i=solve+%5B+e%5Ex%3De%5E10++*+(0.4%2F0.6+)+%5D">https://www.wolframalpha.com/input/?i=solve+%5B+e%5Ex%3De%5E10++*+(0.4%2F0.6+)+%5D</a>
)</p>
<p>Lets make the real world test how often RULE1 is selected with a
act-r model. The model appended in this mail performs 40000
selections (run the command "lisp prob.lisp | grep RULE1 | wc
-l" to count how often RULE1 is selected) and gives to following
results:<br>
</p>
<p>First try: RULE1 is 22671 of 40000 times selected<br>
Second try: RULE1 is 22586 of 40000 times selected<br>
Third try: RULE1 is 22630 of 40000 times selected</p>
<p>Which is every time around 0.56 percent of all selections.<br>
</p>
<pre class="moz-signature" cols="72"><font size="2" face="arial, helvetica">Sincerely,</font>
Kai Sauerwald
---------------------
Knowledge Based Systems
University of Hagen
Univerisitätsstr. 1
58097 Hagen</pre>
<br>
<blockquote type="cite"
cite="mid:mailman.121.1504108827.18986.act-r-users@act-r.psy.cmu.edu">
<pre wrap="">--On Tuesday, August 29, 2017 11:51 PM -0400 Kai Sauerwald
<a class="moz-txt-link-rfc2396E" href="mailto:kai.sauerwald@fernuni-hagen.de"><kai.sauerwald@fernuni-hagen.de></a> wrote:
</pre>
<blockquote type="cite">
<pre wrap="">Hello,
is there a way to archive probabilistic selection of production rules in
ACT-R?
More concrete:? suppose two productions p1 and p2 with the same condition,
how do I have to setup the rules and ACT-R such that p1 is selected with
probability 0.3 and p2 selected with probability 0.7 in conflict resolution?
</pre>
</blockquote>
<pre wrap="">
To do that you would need to set the utilities of those productions and the
utility noise value. The equation that describes the probability of choosing
a production based on its utility, the utility of the competing productions,
and the utility noise is shown in unit 6 of the ACT-R tutorial. Unit 3 of
the tutorial shows how to set fixed utility values using the spp command, and
the parameter for utility noise is :egs as shown in unit 6. Unit 6 also
describes the process through which a model can learn those utility values
based on the rewards it is given.
Hope that helps,
Dan
</pre>
</blockquote>
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