Primacy is one of several memory phenomenon often associated with serial recall--the other most common being the recency effect. There have been several computational models which attempt to establish an integrated account of serial recall (list memory). I will briefly cover to two such models, one ACT-R and one connectionist model.
ACT-R is a hybrid (symbolic and sub-symbolic) cognitive architecture used to model a variety of tasks. It contains a detailed memory module, which is the oldest and most well-validated component in ACT-R (though this distinction does not necessarily apply to its explanation of primacy specifically).
Anderson et al. (1998) explain the primacy effect as an interaction of two mechanisms:
The tendency for the earlier items to receive greater rehearsal
is one factor that is producing the primacy. The other factor is the lower positional confusions among items at the beginning of the list.
The first mechanism, greater rehearsal, refers to the fact that items that are encountered sooner have more time to be rehearsed in working memory. Rehearsal is considered an important component of many influential working memory models, such as Baddeley's model of working memory. Rehearsal in the ACT-R model is accomplished through production rules. Sub-symbolically, rehearsing an item leads to an increase in the base-level activation of a chunk according to the base-level activation equation:
In this equation, a chunk's activation is determined by the frequeny ($n$) with which a chunk is encountered and the recency of each occurence ($t_j$). Rehearsing an item increases $n$, and thus increases its activation level. Chunks are retrieved using the softmax activation function, and neural noise may lead to incorrect retrievals.
The authors justify the use of rehearsal mechanisms, arguing that
In experiments where an effort is made to eliminate rehearsal the primacy effect goes away.
The second mechanism, positional confusion, relies on the fact that each item in the list is stored in a memory trace along with its neighbors. Thus, a memory "chunk" stores not only the item itself, but also the numbers that come before and after it in the list. The partial-matching mechanism in ACT-R leads to memory retrievals in which a neighbor is mistakenly retrieved in place of the item itself. The first and last items of the list have only one neighbor, while items in the middle of the list have two neighbors. Thus, there is an increased chance that numbers in the middle of the list will be transposed.
Botvinick & Plaut (2006) used a recurrent neural network to model list memory. Recurrent neural networks are a common way to model temporal order of events in neural networks. They are also an increasingly popular explanation of how working memory might be implemented in the brain.
Like the ACT-R model, Botvinick & Plaut note the tendency to transpose items during recall:
Note that elements at both the beginning and the end of a list have
fewer positional near neighbors than items toward the middle. This
makes it relatively unlikely that the positions of elements near the
list boundaries will be mistaken for other, similarly represented
Their model also leverages a second mechanism to model the primacy effect, but it is not explicit rehearsal. Instead, it relies on the dynamics of recurrent neural networks to encode earlier items with greater reliability:
Consider that when the first element in a list is
encoded, there are no other elements yet represented in the hidden
layer. When the second item is encoded, there is only one other
element represented there. With each successive element encoded,
the number of elements already in memory continues to increase.
This provides a partial explanation for the primacy effect. As noted
a moment ago, the more items held in memory at any given time,
the more difficult the overall representation becomes to decode.
This means that items at early list positions have an advantage,
because during the overall period from encoding to recall they
share the hidden layer with relatively few other elements.
It is also worth reading Botvinick & Plaut (2006) for their comparison of their own model to several others in the literature, including an earlier version of Anderson's. Briefly, they state:
It is difficult to compare this ACT-R
account with the model we have presented [...]
because several critical aspects of the account (such as the functioning of the position pointer and the basis for similarity between
position representations) are directly stipulated, without an explicit
account of the underlying mechanisms or representational structure. [...]
This being said,
the Anderson and Matessa model, unlike the context-based models
we have cited, can also be viewed as portraying item and position
information as being stored together, as part of a single, structured
representation. If viewed from this perspective, the theory has a bit
more in common with the account we have put forward.
In sum, the two models discussed share some similarities. Both models account for primacy partially through positional confusion during retrieval. The ACT-R relies on explicit rehearsal, whereas the neural network model does not. Though it ignores higher-level strategies, the neural network model can be seen as a lower-level explanation of the primacy effect because it provides a possible explanation of how the effect may arise through the interaction of real neurons.
Anderson, J. R., Bothell, D., Lebiere, C., & Matessa, M. (1998). An integrated theory of list memory. Journal of Memory and Language, 38(4), 341-380. PDF
Botvinick, M. M., & Plaut, D. C. (2006). Short-term memory for serial order: a recurrent neural network model. Psychological review, 113(2), 201. PDF