How Much Information is Too Much?: A Comparison of

Decompositional and Holistic Strategies

Norma P Fernandez & Osvaldo F Morera

University of Texas at El Paso

Making Complex Decisions

A multiattribute decision must have at least two choices from which to choose, defined on at least two attributes.

Meehl (1954) has shown that statistical decision making typically outperforms clinical expert judgment in the diagnosis of patients of MMPI-profiles

Meehl (1954) has influenced how behavioral decision theorists think about complex decision making

Decompoisitional Decision Making

Decompositional Strategy: These strategies break down complex decisions into smaller parts. These smaller parts are then aggregated to derive an overall course of action. One common decompositional technique is

SMARTS (Edwards & Barron, 1994)U(x) = ki u(xij)

The aggregation of attribute weights and utility judgments are often made in a linear fashion such that the overall utility of a stimulus can be calculated, where ki represents the attribute weight and u(xij) represents the single-attribute utility judgment.

Holistic Decision MakingHolistic Strategy

An individual makes one general judgment, while simultaneously keeping in mind all the relevant information during the judgment process, to find the best stimulus.

This strategy is analogous to clinical decision making in Meehl (1954)

Assessing Decompositional and Holistic Decisions

Temporal stability

• In order to measure temporal stability, a participant is given the same stimuli at two different sessions.

• The scores of the stimuli from the first session are correlated with the scores of stimuli from the seconds session.

• While people’s preferences may change over time, it is assumed that the decision strategy with the highest test-retest correlation is the better strategy.

Assessing Decompositional and Holistic Decisions

Convergent validity

We compare two strategies that have something in common.

Convergent validity “is useful to assess the association between decompositional and holistic judgments, and identify factors and circumstances that affect the levels of this association” (Morera & Budescu, 2001).

Decompositional and Holistic Comparisons

As decisions become more complex, holistic temporal stability deteriorates more rapidly than decomposed temporal stability (von Winterfeldt & Edwards, 1986).

Convergent validity is similarly affected by increases in decision complexity (von Winterfeldt & Edwards, 1986).

Present Study

The primary purpose of this project is to investigate the simultaneous effects of attribute complexity and number of stimuli on the temporal consistency and convergent validity of decomposed and holistic judgments.

3 attributes 6 attributes 9 attributes

S1 S2 S1 S2 S1 S2

3 Stimuli (Cars) O1 D-H H-D D-H H-D D-H H-D

O2 H-D D-H H-D D-H H-D D-H

5 Stimuli (Cars) O1 D-H H-D D-H H-D D-H H-D

O2 H-D D-H H-D D-H H-D D-H

7 Stimuli (Cars) O1 D-H H-D D-H H-D D-H H-D

O2 H-D D-H H-D D-H H-D D-H

Present Study

Sample

430 participants (33 did not complete session two)

Mean age 20.57 years old (SD = 4.22).

77.8% identified as Hispanics

58.6% first language was English

52.3% women

Outcome Measures

Temporal stability outcomes: the correlation between holistic (hh) and decomposed (dd) judgments across days, as well as a measure of distance (smaller distance is indicative of increased stability).

Convergent Validity outcome: the correlation between strategies (hd, dh) across days, as well as a measure of distance.

More on the Outcome Meausures

Fisher r-to-z transformation of the correlations

z' = .5[ln(1+r) - ln(1-r)]

Root mean square error (RMS)Measures distance between two decisions

Temporal Stability(Fisher’s r-to-z Transformed

Correlations)

2(order) X 2(gender) X 2(strategy) X 3 (attributes) X 3 (stimuli) mixed ANOVA

Main effect for complexity in attributes (F(2, 376) = 4.77, p = .009, partial 2= .025).

The three attribute condition (M = 1.05) had higher temporal stability than the six (M = .88) and nine (M = .69) attributes condition.

Main effect for complexity in stimuli (F(2, 376) = 3.17, p = .043, partial 2= .017).

The three stimuli condition (M = 1.03) had higher temporal stability than the five (M = .83) and seven (M = .76) stimuli conditions.

Temporal Stability(Fisher’s r-to-z Transformed

Correlations)

Temporal Stability(Fisher’s r-to-z Transformed

Correlations)Main effect for strategy (F(1, 376) = 4.50, p = .035 partial 2 = .012).

However unexpectedly, the holistic strategies (M = .98) were more stable over time than decomposition strategies (M = .76).

Strategy X order X attribute interaction (F(2, 376) = 3.06, p = .048, partial 2= .016)

Temporal Stability:3-Way Interaction

(Fisher’s r-to-z Transformed Correlations)

Strategy X Order X Attribute

HD, DH

Number of attributes

9 attributes6 attributes3 attributes

Est

ima

ted

Ma

rgin

al M

ea

ns

1.2

1.1

1.0

.9

.8

.7

.6

.5

DECISION

Decompositional

Holistic

Temporal Stability:3-Way Interaction

(Fisher’s r-to-z Transformed Correlations)

Strategy X Order X Attributes

DH, HD

Number of attributes

9 attributes6 attributes3 attributes

Estim

ate

d M

arg

ina

l M

ea

ns

1.6

1.4

1.2

1.0

.8

.6

.4

DECISION

Decompositional

Holistic

Temporal Stability(RMS Main Effects)

2(order) X 2(gender) X 2(strategy) X 3 (attributes) X 3 (stimuli) mixed ANOVA

Main effect for complexity in stimuli (F(2, 376) = 4.83, p = .008, partial 2= .025). The three (M = 14.20) stimuli condition was statistically significant from the seven (M = 16.42) stimuli condition. Furthermore, the five (M = 14.02) stimuli condition was statistically different from the seven stimuli condition.

Main effect for strategy (F(1, 376) = 130.24, p = .000 partial 2 = .257). Decompositional strategies (M = 8.96) seemed to have smaller RMS distance values, indicating increased temporal stability than the holistic strategies (M = 20.80).

Temporal Stability(RMS Strategy X Stimuli Interaction)

Strategy X stimuli interaction (F(2, 376) = 3.06, p = .048, partial 2=.016).

A t-test indicated that in the decompositional strategy there was not astatistical difference between the three stimuli condition (M = 9.17, SD= 6.73) and the seven stimuli condition (M = 9.39, SD = 7.31; t(260) = .252, p = .801).

However, in the holistic strategy there was a statistical differencebetween the three stimuli condition (M = 19.42, SD = 13.13) and theseven stimuli condition (M = 23.43, SD = 10.92; t(260) = -2.68, p =.008).

RMS 2-Way Interaction:Strategy X Stimuli

Number of stimuli (cars)

7 stimuli5 stimuli3 stimuli

Estim

ate

d M

arg

ina

l M

ea

ns

30

20

10

0

STRATEGY

Decompositional

Holistic

Temporal Stability(RMS Strategy X Attribute

Interaction)

There was also a Strategy X attribute interaction: F(2, 376) = 8.15, p =.000, partial 2= .042.

A t-test indicated in the holistic strategy no statistical differencesBetween the three attribute condition (M = 20.44, SD = 12.81) and thenine attribute condition (M = 22.28, SD = 12.40; t(254) = 1.17, p =.245).

However, in the decompositional strategy there was a statisticaldifference between the three attribute condition (M = 11.18, SD 8.27)and the nine attribute condition (M = 6.69, SD = 3.72; t(254) = 5.38, p= 000).

RMS 2-Way Interaction:Strategy X Attributes

Temporal Stability

Number of attributes

9 attributes6 attributes3 attributes

Est

ima

ted

Ma

rgin

al M

ea

ns

30

20

10

0

STRATEGY

Decompositional

Holistic

Temporal Stability(RMS Strategy X Order Interaction)

There was a strategy X order interaction (F(1, 376) = 10.58, p = .001,partial 2= .027).

A t-test indicated in the decompositional strategy a non-statisticallysignificant difference between order one (hd, dh; M = 8.40, SC = 6.13)and order two (dh, hd; M = 9.67, SD = 7.16; t(260) = -1.89, p = .060).

However, in the holistic strategy there was a statistically significantdifference between order one (hd, dh; M = 22.08, SD = 11.80) andorder two (dh, hd; M = 19.27, SD = 11.65; t(393) = 2.37, p = .018).

RMS 2-Way Interaction: Order X Strategy Temporal Stability

STRATEGY

HolisticDecompositional

Estim

ate

d M

arg

ina

l M

ea

ns

24

22

20

18

16

14

12

10

8

6

Strategy Order

HD, DH

DH, HD

Convergent Validity (Fisher r-to-z Transformed

Correlations)2 (order) X 2 (gender) X 2 (session) X 3 (attributes) X 3 (stimuli) mixed ANOVA

Main effect for complexity for the stimuli conditions (F(2, 376) = 7.29, p = .001, partial 2= .037). The three stimuli condition (M = .71) had higher convergent validity than the five (M = .38) and seven (M = .34) stimuli condition.

Convergent Validity (RMS)

2 (order) X 2 (gender) X 2 (session) X 3 (attributes) X 3 (stimuli) mixed ANOVA

Main effect for complexity for the attribute conditions (F(2, 376) = 10.06, p = .000, partial 2= .051). The three attribute condition (M = 23.74) was different than the six attribute condition (M = 20.51) and the nine attribute condition (M = 21.01), indicating that increase in complexity leads to less distance.

Session X attribute X order (F(2, 376) = 3.48, p = .032, partial 2= .018).

RMS 3-Way InteractionConvergent Validity

SESSION 1

Number of attributes

9 attributes6 attributes3 attributes

Est

ima

ted

Ma

rgin

al M

ea

ns

26

25

24

23

22

21

20

19

Strategy Order

HD, DH

DH, HD

SESSION 2

Number of attributes

9 attributes6 attributes3 attributes

Est

ima

ted

Ma

rgin

al M

ea

ns

24

23

22

21

20

19

Strategy Order

HD, DH

DH, HD

RMS 3-Way InteractionConvergent Validity

Comparison of RMS and Correlations

Session 1 Session 2 Fisher’s r-to-z RMS

1 30 30 50 50 70 70

Rxy = 1.0 RMS = 0

2 30 30 50 40 70 50

Rxy = 1.0 RMS = 12.91

3 78.18 30 50 50 49.09 80

Rxy = .88 RMS = 33.05

4 21.92 50.71 61.63 53.97 58.12 62.44

Rxy = .42 RMS = 5.12

Which of the two version do you prefer?

BothDecomposedHolistic (Global)

Fre

qu

en

cy300

200

100

0

Subjective Evaluations of Preferences

Future Directions

Order effects may suggest that a replication of this study should be performed where only one strategy is performed per occasion (Morera & Budescu, 1998).

Discrepant findings with RMS and correlations is worthy of future investigation