DECISION MAKING PROCESS: COMPONENTS AND TIME EFFECT

We have seen [here] that the decision making activates a circuit, where the evaluation of the alternative solutions to a given problem and the choice of the best one would give rise to a learning mechanism for error reduction.  

Now let's talk about the main components which influence the decision making (see Figure 1).

We can consider the combination of three factors over the decision making process:

1. the decision environment;
2. the quantity of information;
3. the decision stream.

Figure 1. The components of decision making and the role of the time

Decision making is a process which requires the definition of the informative set (environment) by which select and implement the best solution to a given problem. During the decisional process the quantity of information is cumulated until a certain time (t') beyond which the gathering of more information overload the decision maker. That is, the quantity of the "effective" information does not grow indefinitely, but will decrease from a certain time on. The existence of a time contraint enables the decision maker to get a decision. Decisions may have effect not only at the time when  they have been taken, but also may enter successive decisional processes, i.e., they may feed the decision environment of the same decision maker (or of other decision makers when we consider the social dynamics) in successive times. This flow of information forms the decision stream.    

1. THE DECISION ENVIRONMENT AND THE TIMED   PERFORMANCE

The set of all the information, alternatives, values, and preferences available at the time of the decision forms the so called decision environment.

How should be the "ideal" decision environment ? Well, it would call for all the possible complete and exact information, and every possible alternative should be envisaged !

But the collection of all the information and the identification and evaluation of all the alternatives is "time-consuming" and the time constitutes a bound on the setting of the decisional environment. That is, the time limit produces the break of the learning mechanism involved in the decisional circuit so as to get a decision. On the contrary, an unconstrained decisional time is biologically non plausible since any decision taken at time T+1 would be better (i.e., supported by more information) than a decision at time T. Therefore, it is unlikely that one gets the whole information for making a decision with certainty, so most decisions are taken at the cost of some level of risk. 

According to this scenario we may consider the decision making process as a timed performance framework conditional to the duration of the various options, the duration of the expected delays for receiving the options, and the time constraints for making a choice. [1]

The existence of a time constraint and the perception of the time as a short supplied resource raise the problem of the efficient allocation of time for getting the "right" decision. This results in a typical speed-and-accuracy tradeoff [see here] that the decision makers take on adaptively [2,3]. 

2. THE QUANTITY OF INFORMATION

Delaying a decision as long as possible may return some positive effects:

• it allows the accrual of more information (extension of the decision environment);
• the accuracy of the decisions ("good choices") would be improved;
• new alternatives might be identified (or created). 
• it allows the decision maker to change the rank of the alternatives. 

Conversely, postponing the decision is expected to cause some problems: 

• a too long delay may unbalance the speed-and-accuracy tradeoff and, hence, impair the effectiveness of the decision.
• Gathering more and more information causes information overload: there exists a saturation point in the capability of managing effectively all the information. Thus, the relation between capacity of storing and of managing information is inverse. The state of information overload also involves that the curve of the effective information with respect to the time of accrual, i.e., the quantity of information which can be really exploited in the decision making process, does not grow monotonically but begins to decrease after the saturation point (say, the point t' in Figure 1). Consequently, some of the information would be discarded.
• Too long delayed decisions may strain the decision maker. This would cause a worsening of the ability of taking "good" decisions (accuracy) and/or a selection bias of the information towards non optimal alternative solutions. 

3. DECISION STREAMS

Network of decisions and meta-decision 

"Time is an ever present and prominent dimension in all human decision making. Decisions are oriented towards future time, they take time to make, their consequences develop over time and they are sometimes thought about for a long time afterwards." [4]

Decisions form a network whence the decision makers draw information for proceeding their decisional processes. Actually, decisions may have effect not only at the time when  they have been taken, but also may enter successive decisional processes, i.e., they may feed the decision environment of the same decision maker or of other decision makers when we consider the social dynamics [see also herding behavior] in successive times. This flow of information forms the decision stream.   
Once again, we can note the relationship between time and decision making. Decision streams would give rise to meta-decisions which are decisions we make about decision making: "when should this decision be made?", "how long this decision take?", "how much time have decisions like this one taken in the past?",... [3,5]
In other terms, decisions are made in a context (network) of other decisions, such that each decision may be supported by the decision stream formed in other times and/or by other subjects (sharing experience). 
The main advantage of this stream of decisions is that by providing the decision maker with a "template", it speeds up the choice towards proved rewarding solutions [see here]. 

ITALY'S FOREIGN TRADE 2012

The performance of the foreign trade of Italy during the last part of year 2012 has been exhibited in positive  terms by the majority of the mass media and politicians in Italy. In particular the  alleged "good" performance has been attributed (at least indirectly) to the financial measures adopted by the government led by Mr. Monti. 

But the value of the trade expressed in monetary units can be better understood if we consider the two factors that compose them:

• the amount (volume) 
• the average unit value (AUV) which is an estimate of the average prices of products exported (imported) in a certain period.

By looking at the data presented by the Istat (Italian National Institute of Statistics) on Italy's foreign trade as well as unit value and volume indices (base year 2005=100) referring to October 2012 results in a useful argument for analyzing the foreign trade. 

In the following plots there are shown the results of some simple statistical analysis conducted on the ISTAT data on foreign trade in the period ott2010-ott2012. 

1. Volumes (Vol) and AUV are expressed as numbers fixed base index (data year 2005 = 100).
2. The analysis of these two variables have been carried on by considering two sub-periods: oct2010:oct2011 and oct2011:oct2012, which in practice allow a comparison between two actors of Italian politics: Mr. Berlusconi and Mr. Monti.
3. The straight lines of the linear regressions applied to series Vol and AUV were tested for significance of differences between their angular coefficients and their intercepts.
4. To compare the values of Vol and AUV in the two sub-periods the signed rank Wilcoxon test has been applied. 
5. To evaluate the presence of trends in the series was used  the Cox-Stuart test (as described in [1,2] ).
6. All the statistical tests were two-tailed and the significance level was fixed at 5%.

1. VOLUMES AND AVERAGE UNIT VALUES

Figure 1. Italy's Export vs. Import: Volumes

Test on slopes and intercepts

Are the slopes equal?

F = 0.000763418. DFn=1 DFd=22

P=0.9782

If the overall slopes were identical, there is a 98% chance of randomly choosing data points with slopes this different. You can conclude that the differences between the slopes are  not significant. 

Since the slopes are not significantly different, it is possible to calculate one slope for all the data.

The pooled slope equals 0.87743

Are the elevations or intercepts equal?

F = 5.84636. DFn=1 DFd=23

P=0.02393

If the overall elevations were identical, there is a 2.4% chance of randomly

choosing data points with elevations this different. You can conclude that the differences between the  elevations are significant. 

Comment at the Figure 1: 

in the two compared periods  the coverage rate (Export / Import) of the Volumes represented by the slope of the linear regressions remained unchanged (0.87). 
During the second period, however there is a significant shift in the upper left of the regression line. This due to the significant decrease in the volume of import in the same period oct2011-oct2012.



Figure 2. Italy's Export vs. Import: Average Unit Value

Are the slopes equal?

F = 1.91779. DFn=1 DFd=22

P=0.18

If the overall slopes were identical, there is a 18% chance of randomly choosing  data points with slopes this different. You can conclude that the differences between the slopes are  not significant. 

Since the slopes are not significantly different, it is possible to calculate one slope for all the data.

The pooled slope equals 1.29806

Are the elevations or intercepts equal?

F = 15.0005. DFn=1 DFd=23

P=0.0007706

If the overall elevations were identical, there is a 0.077% chance of randomly  choosing data points with elevations this different. You can conclude that the differences between the  elevations are extremely significant. 

Comment at the Figure 2: 

in the two compared periods  the coverage rate (Export / Import) of the AUV represented by the slope of the linear regressions remained unchanged (1.29). 
During the second period, however there is a significant upward shift of the regression line.

Figure 3. Italy's Export Volumes: two periods compared

Figure 3 casts some doubt about the fact that during the second period the volume of the exports have increased. Let's see then the following plot:





Figure 4. Comparing the Italy's Export Volumes between the two periods

The statistical test of Figure 4 indicates that there is significant difference in the export volumes between the two periods considered. Specifically, during the first period oct2010:oct2011 the median level of the export volumes resulted higher than the one measured in the second period. 

Maybe the performance of the Italy's export in the last part of 2012 has been determined by the effect of the AUV (Figure 5):

Figure 5. Italy's Export Average Unit Value: two periods compared

The statistical test (Figure 6) confirmed that the export AUV in the second period have been significantly higher than the export AUV in the firts period.

Figure 6. Comparing the Italy's Export Average Unit Value between the two periods

2. TERMS of TRADE (ToT)


The Terms of Trade (ToT) is given by the ratio:

      Price of export / Price of Import 

ToT is an effective indicator of the difference between the average export prices and import prices. Usually an increase in ToT is referred to as an "improvement" as the prices of exports would increase by more than imports. 

But beyond a certain threshold the increase of ToT can introduce bias, because it would favor an increase in the prices of exports and therefore tend to be reduced in volume. On the contrary it tends to favor imports as becomes more affordable.

Since ToT is given by the ratio between the amount of money, it can vary both in function of the relative prices of goods exported vs. imported at the same exchange rate, and in terms of the change in the exchange rate (for example euro vs. U.S. dollars) at unchanged prices of goods. 

So as the relative devaluation of the domestic currency yields benefits in the trade balance, it is necessary that the sum of the elasticities of exports and imports relative to the exchange rate is greater than 1: it is the necessary and sufficient condition described by Marshall-Lerner   [see video below for explanation of the Marshall-Lerner condition].

Here the ToT has been approximated by the ratio: 

AUV Export/AUV Import

Figure 7. Italy's Terms of Trade: two periods compared

The ToT in the period oct2011:oct2012 has resulted greater than in the previous period (Figure 8).

Figure 8. Comparing the Italy's Terms of Trade between the two periods

From Figure 7 it is visible that in the trimester from August 2012 to October 2012 the course of ToT has decreased so as to be indistinguishable from the values observed in the homologous trimester of 2011. That is, also the AUV of import (with respect to the AUV of export) has increased.  


3. THE ADJUSTED TRADE BALANCE


The Adjusted  Trade Balance (ATB) is obtained by calculating the following ratio between exports and imports expressed in monetary values​​:

ATB = 100 * (Export-Import) / (Export + Import)

Hence, ATB takes values ​​between -100 (when the country is uniquely importer) and +100 (when the country is uniquely exporter). If the trade balance is in equilibrium, then ATB = 0.
The performance of the normalized trade balance is increasing if exporting has a growth rate higher than that of imports. In Figure 9 it is drawn the Italy's ATB for the two periods. The results seems to be related to the increasing of the export AUV between oct2010:oct2011 and oct2011:oct2012.

Figure 9. Italy's Adjusted Trade Balance in two periods

4. TESTING FOR THE TREND

The Cox-Stuart test here(Table 2) is used to distinguish the overall performance of trade flows between the two periods. The results are significant, with p value = 0,0156. 

In the first period oct2010:oct2011, there is a growing trend in the trade balance both in terms of volumes and in terms of AUV. Also the course of theToT and ATB have rising trend. In the following period, we note significant trends from the import. Specifically, there is downward trend in import volumes and import growth for AUV.

The main conclusion is that:

neither the first period nor the second period shows trend in the export data. That is, the ramping of the export AUV for both periods as displayed in Figure 5, is not significant.  

Table2. Trend (Cox-Stuart test)

oct2010:oct2011        oct2011:oct2012

Export:Vol                             no                                 no

Export:AUV                          no                                 no

Import:Vol                            no                                  -

Import:AUV                         no                               ­   +

Trade Balance: Vol               +                                  no

Trade Balance: AUV            +                                  no

Terms of Trade                    ­+                                  no

ATB                                       +                                   no


5. CURRENT ACCOUNT BALANCE 

In order to get a better picture of the dynamics of the italian foreign trade it is necessary to wait for the publication of the 2012 Current Account Balance, that in 2011 closed with a deficit of 72 419 millions USdollar (value seasonally adjusted)  [see here  OCSE data set]. See also Figure 10 below.

It is well known, in fact, that a negative balance means that the revenue currency are not enough to cope with the outflow, and if a country needs to import because of the lack of raw materials, necessarily will need to gear to also increase its exports in order to balance the account. In fact, you can not draw on reserves indefinitely. The reserves are likely to run out, and can not be used for commercial deficits of long duration (also called structural).


It is therefore necessary redress the balance, and this can be done in several ways:

1. through the so-called "structural adjustment policies", which basically aim to reduce imports by decreasing domestic demand by lowering the private and public spending, and to boost exports by reducing labor costs. The IMF loans are conditional on the implementation of these policies, which involve a heavy internal crisis for the country that has to bear.
2. a typical solution is to resort to protectionist policies, which make imports more expensive applying customs duties, or by acting indirectly support with subsidies for domestic production so that it is more competitive than foreign products, it may also restrict or prohibit by law the importation of certain goods, in one way or another, this kind of policy can trigger trade retaliation by other countries then make exports more difficult.
3. The interest rate has an influence on the balance of payments, because if the trade is in deficit, raising the official interest rate can attract capital from abroad in search of good returns and redress the balance with a surplus of movement of capital. It should be noted that a rise in interest rates has a depressing effect on the economy of the country, making it difficult investment and credit - which may indeed also be useful for the purpose of balancing the trade balance, because a depressed economy matter less.
4. The solution absolutely typical, in the context of a flexible exchange rate, is the competitive devaluation. Devaluing the exchange rate, you make it more expensive for foreign currencies and therefore imports, while exports become cheaper, so as to balance the scales (In a nutshell: the exchange rate).

Figure 10. Italy's Current Account Balance: period 2005:2012

Source: Bank of ItalyData are reported in billions euro.
After the nineties, starting from 2000, the current account balance recorded deficits again, with an irregular, but tends to get worse. In particular, in 2008, the current account deficit reached 3.41% of GDP, the worst figure since 1981, before falling slightly in 2009 (3.16%).

EURO ZONE GDP DOWN BY 0.6%

GDP fell by 0.6% in the euro area (EA17) and by 0.5% in the EU27 during the fourth quarter of 2012, compared with the previous quarter, according to flash estimates published by EUROSTAT, the statistical office of the European Union. 
In the third quarter of 2012, growth rates were -0.1% and +0.1% respectively.

This is the synthesis on the (bad) status of the Q4 GDP released today by EUROSTAT [read document]. 

Figure1. The time course of GDP: Q1 2006 - Q4 2012

Table1. Quarterly growth rates of GDP in Europe.

The data confirmed the downward trend in both the EA17 and the EA27 areas. What worries the market analysts is that the worsening of the Q4 GDP is larger than it was unexpected. Only for Germany seems likely to observe during the rest of 2013 a GDP growth. 
Meanwhile France has announced that in 2013 the target of the 3% GDP deficit will be dissatisfied. 
Things are expected to get even worse for the other Euro peripherals countries. Spain and Italy are in deep water. 

In Spain:

• The government is extremely unpopular and it still has many unpopular spending decisions to take. Domestic tension remains high and with still rising unemployment, it could get worse. Which could spawn yet more anti-centralisation from the regions.
• Lowering Spain wages has made Spain more “competitive”, but only in European wage terms.
• Unfortunately, Spain’s only competitive "advantage" is lower wages: Spain isn’t a leader in the value-added factors of mature European economies;
• While European manufacturers may well be looking to move production to Spain because of low wages, it doesn’t help the strong Euro makes the whole country uncompetitive  on the world stage, and that European consumers aint consuming very much.
• Emigration of the best and brightest adds to the demographic time bomb ticking in the Spain pension funds.
• Although the 25% plus Spain unemployment probably underestimates the black economy – it’s a simple fact the whole Spanish private sector is massively overleveraged, especially as family heads are losing their jobs. Falling wages and job losses increase the burden. Banks remain massively vulnerable to rising retail distress.
• All the above without even mentioning fact the economy is burdened by millions of unsellable homes with no one likely to buy. 

In Italy:

• The result of the coming soon election upsets the Euro "elites".
• In the course of the last year, the financial measures adopted by the Monti's government have torn down the manifacturing capability of the country. 
• Around ninety thousand firms have ceased their activity in 2012 and twelve thousand have gone bankrupt. 
• The industrial production in 2012 has fallen by 6,7% (Figure 2)
• The consumption of energy power has decreased by 5,6%. (Figure 3)
• Automotive fuel products, with a delivery day more, have identified the following factors: the gasoline in the complex showed a decline of 13.7% (-95,000 tonnes) compared to January 2012, and the transport diesel by 5.3% (-98,000 tons). (Figure 4)
• Italy, along with Greece, Spain, Malta and the Baltic States, is part of the group of countries where "there is a high risk of entering into poverty and low chance of getting through the creation of a massive poverty trap". This critical social issue has been described by Lazlo Andor (EU Commissioner for Social Affairs) in the 2012 EU report on unemployment and social developments [here]
• The employment rate (61,2%) is one of the lowest in EA27. Only Greece (59,9%) and Hungary (60,7%) show rates of employment worse than Italy. (Figure 5)

Figure 2. Industrial production in Italy december 2012 - december 2012

Source:  Italian National Institute of Statistics (ISTAT).

The red curve represents the monthly seasonally adjusted index. The gray curve is the moving average (three terms)

Figure 3. Consumption of power energy (billion kWh)

Source: Terna (The Terna Group is the first grid operator for electricity transmission in Europe. )

In the horizontal axis the monthly values. 

Figure 4. Consumption of oil products in Italy 2006 - 2012

 In black and gray are drawn the trend lines.

Figure 5. Employment rates vs. Unemployment rates

The "therapy" that the Monti's government has dictated to the country undoubtedly has failed and has severely affected the italian society as well as the italian economy.  

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A Continuous Semantic Space Describes the Representation of Thousands of Object and Action Categories across the Human Brain

"Humans can recognize thousands of categories. Given the limited size of the human brain, it seems unreasonable to expect that every category is represented in a distinct brain area,”

says first author Alex Huth, a graduate student working in Dr. Jack Gallant’s laboratory at the University of California, Berkeley.

In a video diplayed at the web page of NEURON [link to the  article], the author reports how 

objects and action categories are organized within the brain according to a continuous  semantic space throughout the cortical surface.


Dr. A.P. Masucci (Research fellow at the Centre for Advanced Spatial Analysis CASA, University College of London.) defines [here] the semantic space as: 

 "the space of meaning, where the dynamics of meaning keep place. Where is it? It is in our heads!! Language is a collective phenomena and it resides in all our heads. As a natural phenomena language follows its natural laws and self-organises in structures and hierarchies."

The Drift Diffusion Model (DDM) for Decision Making in the TAFC task

In applying the diffusion model to the TAFC, it is assumed that the accrual of noisy evidence corresponding to the two alternatives (e1, e2) is carried on until their difference (e1–e2) reaches a decisional threshold at the upper value (Th) or at the lower value 0. The attainment of one of these critical values indicates where the preference is directed: the upper threshold relates to the positive sign of the difference (e1–e2), while the lower thresholds corresponds to the negative value of (e1–e2). 

The time necessary to reach one of the boundaries, i.e. the response time RT, depends on:

a) the distance between the boundaries and the starting point; 

b) the drift, i.e., the rate at which the average (trend) of the random variable (e1–e2) changes; 

c) the diffusion, i.e., the variability of the path from the trend (Figure 1). 

These elements characterizes the so called drift diffusion model (DDM). The accumulation of evidence is driven both by a deterministic component (drift) that is proportional to the stimulus intensity and by a stochastic component of noise that makes the evidence deviate from its own trend. The variance of the noise is the diffusion parameter of the model. 

The rationale of DDM is that since the transmission and codification of the stimuli are inherently noisy, the quality of the feature extraction from such inputs may call for  accumulation of a sufficient large sequence of the stimuli to get information [1]. By knowing the threshold level and the RT enables one to take a sight into the mechanism underlying the decision process [2,3]. 

Figure1. The randomness of the path taken under the influence of noisy stimuli characterizes the  diffusion models. A stimulus is represented in a diffusion equation by its influence on the drift rate of a random variable. This random variable, say the difference of evidence corresponding to the alternatives, accumulates the effects of the inputs over time until one of the boundaries is reached. The decision process ends when evidence reaches the threshold and the time at which it occurs is called response time (RT). Therefore, the drift term represents the weight of evidence in favor of one alternative. The variance of noise in the input signals determines the  diffusion of the path of the random variable. We can draw an analogy with a physical system and imagine the decisional process as the state of a “particle” moving within a potential well. Under this point of view, the persistence for relatively long periods of the state variable in the sub-threshold area implies that the particle still entangled in the potential well, enters an excited state where it remains for an exponentially distributed time interval with a certain decay time τ_d. If the combination of input and noise is sufficiently strong, then the particle is able to jump the barrier, i.e. the threshold, and the system returns to an equilibrium state. The dynamics of the particle thus may resolve in a relaxation process [4] characterized by the oscillations between periods of sub-threshold “disorder” inside the potential well and short impulses that trigger the system beyond the threshold in the rest state. This physical analogy allows to better perceive how the DDM may fit the evolution of the input-output map underlying the neuronal model of the decision-making process.

It has been shown [5,6] that under experiments with human subjects performing TAFC tasks, the DDM yields accuracy and reaction times (RTs). Moreover, the RTs estimated by the DDM tend to distribute as an asymmetric random variable, that is, so as it would be expected from human performance, because the RT distributions are usually skewed toward longer times. An advantage from DDM is that, given a level of accuracy, it results the fastest decision maker, for a fixed decision threshold. 

The noisy signals emphasize the role of the thresholds, in fact, thresholds have no effect on accuracy if the noise is absent. Instead, the noise makes the variable representing the difference of evidence corresponding to the alternatives, stochastic. The fluctuations of this random variable generates series of erroneous responses, and the response times refer both to the correct and to error responses. The accuracy tends to increase proportionally to the rising of threshold which results in a speed–and-accuracy tradeoff. 

The speed-and-accuracy tradeoffs are usually reproduced by adjusting the boundaries such that lower thresholds produce faster but less accurate responding, whereas higher thresholds produce more accurate but longer decision times in order to average out uncorrelated noise. This speed–accuracy trade-off is usually considered a basic parameter for interpreting the results both of behavioral experiments and, as before reported, neurological experiments [2,7,8]. However, the surprising capability of DDM to fit behavioral and neurological data seems to indicate that some decision making process in the brain are really computed by a similar mechanism that accumulates evidence [9].