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Using Collective Decision System Support to
Manage Error in Wireless Sensor Fusion
Arnold B. UrkenProfessor of Political Science
Stevens Institute of Technology
Hoboken, NJ [email protected]
Presented at Fusion 05, the International Conference on Information Fusion, Philadelphia, PA., July, 2005.
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Using Collective Decision System Support to
Manage Error in Wireless Sensor Fusion*
Arnold B. UrkenProfessor of Political Science
Stevens Institute of TechnologyHoboken, NJ [email protected]
Abstract When sensor fusion uses voting methods to
produce collective decisions on the basis of incomplete
and imperfect information that would be produced if
voting information were perfect and complete, the
collective outcomes will be error-resilient. Theseoutcomes will not be changed by breakdowns in wireless
network communications or decision making errors.
Error-resilient collective outcome (ERCO) analysis
makes it possible to predict how long to wait or how
many votes to reach an optimal collective decision.
ERCO analysis also provides a new framework for
gaining strategic and tactical advantages from network-
centric information sharing. This framework raises new
theoretical and empirical research opportunities for
integrating voting theory and fusion research.
Keywords: wireless sensor networks, distributeddetection, error, decision fusion, voting systems, error-resilient.
Patent pending. Portions of this work were supported bycontract DAAE30-00-D-1011 to the Stevens Wireless
Network Security Center, 2004. Approved for GeneralPublic Release.
1 Introduction
Current developments in the design and deployment of
sensors are challenging existing methodologies for
collecting data and producing useful information inwireless networks. In commercial and security
applications of sensor technology, producing precise and
accurate intelligence is being constrained by new
standards for reliability, cost, processing speed and
energy conservation. Although voting methods have
been used to address problems of sensor communications
in networks, sensor fusion techniques have not been
developed to overcome errors caused by breakdowns in
network communications and faulty decision making.
This paper outlines a new approach to wireless sensor
fusion that uses voting systems to manage these errors.
The paper is organized to explain how voting system
can be designed to provide error-resilient sensor fusion.Section 2 provides a framework that explains the
motivation for developing a new approach and
summarizes the state of the art in building error
management into voting processes. Section 3 presents
the concept of an error-resilient collective outcome
(ERCO) and explains how voting systems can be
designed to measure ERCO efficiency for complex
decision tasks in risky network environments. In these
systems, voting methods are used to answer different and
complementary questions about the same data. Section 4
applies this theoretical approach to a complex decision
task in which voter ratings are processed throughplurality, approval, and Copeland scoring methods in a
Monte-Carlo simulation to compare their ERCO
efficiency. And Section 5 discusses the simulation
results and outlines key questions for future research.
2 Sensor Design and Deployment
New sensor designs and deployment plans are driving
forces in the evolution of sensor fusion techniques. For
example, sensors that use light-scattering technology to
identify and detect more than one agent have led to
proposals [1] for deploying large sensor arrays ofmultipurpose sensors in cities to provide protection
against NBC (Nuclear, Biological, and Chemical)
attacks. These deployments could provide early
warnings that enable targeted populations to take evasive
action and permit first responders to mitigate damage.
Innovative use of materials is extending such
capabilities by creating smaller, mobile, and inexpensive
sensor systems that can increase the scope and accuracy
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of multifaceted data that can be collected to produce
knowledge [2]. By understanding the underlying
complex patterns in such artificial environments, controls
can be designed to generate precise and accurate sensor
information.
However innovations in the ability of sensors to
produce complex knowledge have not taken full account
of the problems of producing information in wireless
networks. Sensor capabilities are limited by decision-
making and transmission errors. Physical interactions
with sensed environments can degrade sensor reliability
and speed in detecting phenomena. Even if sensor
performance is not degraded by environmental
conditions, technology costs and energy constraints may
limit the feasibility of deploying enough sensors to
monitor a situation.
Moreover, when sensors are not attacked by physical or
cyber attacks, the wireless networks that are needed fortransmitting data and producing knowledge pose risks.
Data collection can be thwarted by malicious actions that
divert messages to the wrong destination or overwhelm
the processing speed and energy constraints provided by
network architecture. Although malicious attackers can
use commercial jamming devices to thwart wireless
communications, the same effect can be caused
inadvertently by environmental distortions from
background radiation from buildings.
For these reasons, decision fusion should not be
considered an afterthought in the development and
deployment of new techniques for sensor knowledge.Error should be integrated into the design of wireless
sensor architecture. Wireless systems based on such
designs will facilitate the development and deployment
of innovative sensors in two ways. First, they can remove
obstacles that limit deployment of emerging sensor
techniques for producing more complex intelligence.
And second, wireless sensor systems that are resilient to
error will enable designers of sensors to increase the
complexity of inputs that can enhance the scope and
accuracy of knowledge.
2.1 Voting, Error, and Decision Fusion
Sensor fusion models have been developed to plandecision tasks and the collection of sensor data, address
the ontological basis of fusion processes [10], use
Bayesian techniques to manage the integration of sensor
data [13], and design local sensor decision thresholds to
maximize detection performance [12]. Fusion models
that have used voting systems to achieve similar analytic
objectives [11] have drawn from voting theory as well as
theoretical insights about processing data in computer
networks [4, 5]. Each of these analytical perspectives
addresses the problem of error in different ways, though
neither perspective incorporates the concept of error-
resilient fusion into the voting process itself.
The computer science and computer engineering
literatures have used voting methods in sensor fusion
because processing of votes does not require much
bandwidth or computational overhead. With notable
exceptions [6], applications of voting systems are
confined to the use of simple methods of weighting votes
with majority rule to control sensor fusion processes. In
these studies, there is usually a focus on how to weight
the votes.
Voting systems contain subsystems that enable
individual voters to communicate information about
preferences and judgments to form a collective outcome.Each voting system contains subsystems based on rules
for the endowment of votes that can be used to express
individual information, rules for the allocation of votes,
and rules for aggregating votes to create a collective
outcome. For instance, plurality voting, commonly
used in elections in many Western democratic polities,
includes an endowment of one vote, an allocation
constraint that restricts assigning the vote to a single
choicenormally without splitting or saving the vote
and a plurality aggregation rule that recognizes the
choice with the most votes as the winner.
Computer scientists counterbalance the application ofvoting methods with techniques for managing problems
caused by breakdowns in network communication that
prevent the production of collective outcomes. For
example, statistical techniques are used to remove clutter,
cleanse data, and weight votes. These techniques depend
on the assumption that data collection satisfies
quantitative and qualitative requirements necessary for
the application of statistical methodology. These
requirements entail the creation of networks that are
computationally intensive, energy inefficient, and
dependent on sequential sharing of information [7],
In the theoretical voting literature, where elections arethe focus of analysis, the most common assumption is
that votes are collected successfully to produce a
collective outcome that reveals the group preference.
Problems in voting theory, social choice, and collective
decision making analyses focus on how to process the
voting data once it received so that collective outcomes
with particular attributes can be created. And although
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voting theorists often disagree about the properties of
these attributes, the question of what happens if votes are
missing does not normally arise in arguments for or
against the use of a voting method [9].
In pre and post-election surveys sampling and data
cleansing techniques are used to deal with missing data
by making a priori assumptions that permit the creation
of stratified samples. But voting analysts focus on
problems of preference aggregation such as paradoxical
and manipulated collective outcomes. Outside of the
preference aggregation mainstream, voting theorists who
address the problem of voter error by weighting
individual votes based on the cognitive ability or
competence of each decision maker. Neither of these
analytical traditions of voting analysis considers what to
do if and when error caused by network communications
breakdown occurs. If all of the votes cannot be
collected, group preferences cannot be inferred andindividual voter preferences cannot be weighted to
optimize group performance.
Neither the voting literature nor the computer science
literature builds error-management into the vote-
collection process itself [2]. Integrating error
management into voting process design makes it possible
leverage communication in the network applications
layer to improve wireless sensor fusion. By interpreting
network communications from the viewpoint of the
recipient of votes, incomplete and imperfect voting data
can be transformed into instantaneous and accurate
information. Understanding the complex patternsunderlying such voting transactions can be used manage
sensor decisions in risky network environments.
3. Error-Resilient Voting Analysis
This section provides a formal definition of an error-resilient collective outcome (ERCO) and explains howto analyze voting systems to compute the probability of
producing ERCOs.
3.1 What is an ERCO?
An ERCO, error-resilient collective outcome, is avoting outcome based on incomplete and imperfect
information that would be produced if information about
the voting situation were complete and perfect. Humans
make intuitive use of ERCOs in simple situations. For
example, suppose a central commander relies on ten
sensors to report whether an object is A or B and bases
an inference on the majority outcome. If the commander
has already received 6 votes in favor of A, then the
outstanding 4 votes cannot change the collective
outcome. The score in favor of A may increase or stay
the same, but the outcome cannot be changed by lack of
information caused by network communications and/or
sensor errors.
In our hypothetical convoy assessment example with
only two choices, six votes satisfied the aggregation
requirement to make choice A an ERCO. However
ERCO-based distributed inference provides a generic
form of automated decision support that enables
commanders to manage risk and uncertainty when the
collective outcome is not as clear-cut as it is in our
hypothetical example. For instance, suppose that the
commander has received 5 votes in favor of A and 2
votes in favor of B. In this case, the commander must
either wait to receive more voting information or make
an inference that might be very risky and
counterproductive. In such complex situations, it is notclear if the outstanding information has been delayed by
network traffic or if breakdowns in network
communications or sensor failures have caused the
problem. Under such conditions, without collective
decision system support, commanders may unwittingly
avoid risky choices that are reasonable and make risky
choices that are unreasonable.
For more complex, non-binary decision tasks, ERCOs
can be defined for collective decisions with two or more
choices for a fixed number of human or machine sensor
voters and an aggregation rule that determines that a
decisive collective outcome has been produced. At eachstage of data collection, the number of outstanding votes
in the network can be represented in terms of the
percentage of the total number of voters or time required
to collect a particular segment of the outstanding votes.
If at any stage of the process of collecting votes, the
number of collected votes satisfies the aggregation rule
and the collective outcome cannot be changed by receipt
of any combination of outstanding votes, then the
collective outcome is an error-resilient collective
outcome (ERCO).
ERCOs can be produced for choices on single or
multiple dimensions for collective decisions that takeplace in client-server or peer-to-peer computer
networking environments [8]. However this paper
describes ERCO production for a complex decision task
along a single dimension: the number of vehicles in a
convoy.
Regardless of the cause(s), the costs of waiting can be
significant. Lives and property will be lost and
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opportunities for redeploying resources to counterattack
or take evasive action will be missed. And emergency
responders will not receive early warnings to prepare to
care for victims.
3.2 Designing ERCO-Efficient Processes
The probability of producing an ERCO depends on the
voting system used to process voting data and produce
collective outcomes.
3.21 How Voting Systems Work
Ratings, inputs for a voting system, can be based on
ordinal or cardinal scales. These inputs are processed
according to rules for communicating the rating
information, converting this information into votes and
aggregating the results into a collective outcome. Ratingcommunication depends on vote endowment and
allocation rules that govern the expression of rating
information.
The vote endowmentfixes the number of votes that can
be used to express ratings while the vote allocation rule
sets constraints on the allocation of the endowment. The
aggregation rule determines how many votes are
required to form a winning coalition.
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The following chart illustrates the definition of these
rules for three systems.
The OPOV system, a fully-specified description of
plurality voting, reveals which choice is most
frequently top-ranked in voter ratings. Approval voting
(AV) shows which choices are approved (or disapproved)by a plurality or majority of voters. And Copeland
voting reveals the relative collective intensity of
preference that voters express in their ratings.
Although voting theorists debate which voting system
is best, each system answers different questions about the
collective outcomes produced by the same voting or
rating inputs. All voting systems may have paradoxical
attributes and do not necessarily generate consistent
collective outcomes.
Consider the processing of the following voter cardinal
ratings for three choices, A, B, and C.
When these inputs are processed in a OPOV system with
plurality rule, the allocations are
and the collective outcome is a three-way tie, a
phenomenon associated with the paradox between
individual and collective transitivity.
When the original inputs are processed in AV and
voters cast one approval vote for each choice that equals
or exceeds their average rating, the vote allocations are
Table 1Subsystems of Three Voting Systems
Table 2Hypothetical Voter Rating Scenario
Table 3Conversion of Ratings into Single Votes
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and B is the plurality winner (based on the definition of
the aggregation rule determined by the number of voters
who expressed approval (3 out of 3), which would not
satisfy the requirement of a majority of the total number
of allocated approval votes).
Under Copeland voting with plurality rule, the ratings
are first processed with Condorcet scoring, which
computes the number of times that each choice is ranked
higher than every other choice in voter preference
ratings. These Condorcet scores are
Table 5Conversion of Ratingsinto Condorcet Scores
Copeland scores are then computed by subtracting the
Condorcet scores to produce
Table 6Derivation of Copeland Scores
This illustration shows that voting systems can produce
inconsistent collective outcomes, but also generate
collective outcomes with different scores with consistent
relationships. For example, B wins under AV and
Copeland voting.
ERCO Production
The following example shows how voting systems
produce ERCOs under OPOV system; the results for AV
and Copeland voting follow the same logic and are
presented below.
In this example, ten sensors (including acoustic (AC)
and infrared (IR) sensors) provide feedback to a
commander to collectively identify the number of
vehicles in a convoy so that the commander can
determine if an attack is reasonable. The sensors report
the correct number of vehicles by rating an overlapping
set of choices (from 0 to 4 vehicles) on a 0-10 scale, as
shown below.
Table 4Conversion of Ratings into Approval Votes
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Table 7Sensor Ratings for
Convoy Assessment Task
When these ratings are converted into OPOV allocations,
as shown below in Table 8:
Table 8OPOV Allocations based on Table 7
there is no majority winner (since 4 vehicles receivesonly 4 out of 10 votes), leaving the commander, C2,
without advice about whether to attack. And if IR1s
ratings are not received, the commander would be faced
with a tied collective outcome.
In this type of decision scenario, if all of the sensors
were equally competent, ERCO analysis would focus on
the probability of satisfying the aggregation rule at any
point during the voting process. However sensors have
diverse competencies in detecting objects depending on
the manufacturers specifications and sensor limitations
caused by different operating conditions. So we will
assume that the ERCO objective is to produce acollective outcome that optimizes the group probability
of making a correct collective choice with complex
preferences and competencies. In this scenario, sensor
votes can be weighted using the Shapley-Grofman
theorem [10], which assigns weights to votes based on
sensor competence or reliability using the following
formula:
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ln(p/1-p) (10),where
p = probability of a correct choice (11)and
(1-p) = the probability of an incorrect choice (12)If p=.2 for sensors AC1-AC3, .5 for sensors AC4-
AC6, and .8 for sensors IR1-IR4 have a .8 competence,
the following chart shows the Shapley-Grofman (SG)
[10] weights that would be used to adjust the value of the
votes in Table 8:
Table 9Shapley-Grofman Weights
And the sensor votes in Table 8 would be transformed as
shown below:
Table 10Sensor OPOV Allocations
Based on Tables 8 & 9
with the 4 vehicles choice identified as the winner
under plurality or majority rule.
Table 11Example of an ERCO
In this scenario, if the votes of AC2 and AC6 are not
received, 4 vehicles would be an ERCO.
4. Monte Carlo Analysis
To investigate the probability of producing ERCOs under
OPOV, AV, and Copeland voting systems, Monte Carlo
experiments were conducted in Mat Lab. Random
variables include voter ratings (homogeneous or
heterogeneous), decision competencies, and the time
required for each set of voting information that
successfully makes it from a sensor to the commander to
form a collective outcome. Shapley-Grofman weights
are used to adjust individual votes and time is
represented by a Rayleigh distribution with a mean of 5seconds.
The following results are based on 20,000 runs for 100
sensors in a bimodal culture. In this culture, 75% of the
sensors have homogeneous ratings and a high (.9)
competence, and 25% of the sensors have heterogeneous
ratings with a competence of .48. This scenario is typical
of situations in which sensor disagreement can lead
decision makers to take unreasonable risks. In such
cases, human consumers of sensor fusion may be forced
to rely on experience or intuition to resolve sensor
disagreement. When only 1 or 2, sensors disagree,
educated guesses may be reasonable, but, as in ourscenario, when 25 out of 100 sensors disagree, additional
decision support is needed to augment human
capabilities.
In each simulation run, a group of voters are randomly
selected from a randomly chosen set of 100 voters that
are drawn from a population with the bimodal cultural
preference, competence, and vote transmission time
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attributes associated with our scenario. Then voters are
randomly selected to simulate the process of votes
arriving at C2 (Command & Control) from distributed
sensors. After a vote is received, the simulation finds the
collective outcome under OPOV, AV, and Copeland
voting methods and counts the number of times that a
given collective outcome would be produced if all of the
votes were collected. These counts are correlated with
the proportion of outstanding votes and the cumulative
vote transmission time associated with each ERCO.
Then the counts of successes and failures in ERCO
production are used to compute the probability of
producing an ERCO. This probability can be used to
compare the ERCO efficiency of voting systems under
different scenarios.
Ties can occur under all voting systems, though the
probability of generating a tie is greater under some
voting systems. For example, when preferences areheterogeneous, the probability of a tie is greater under
AV than it is under OPOV or Copeland voting systems.
The simulation results reported here are based on the
assumption that ties are randomly broken. This
assumption increases the performance of the AV system
more than it improves the ERCO-efficiency of OPOV
and Copeland systems. Ties could also be resolved
optimally by, for example, by selecting the Copeland
winner in a tied set if one existed.
Other control variables such as false positive and false
negatives are kept low and constant in the results
presented in Figures 1-4 (below). All of these scenariosare based on the same initial conditions for a simulation
run, but Figures 1 and 3 include homogeneous (similar)
ratings or preferences, while Figures 2 and 4 show what
happens when ratings or preferences are heterogeneous
(diverse).
Although all of the simulation results show that ERCO
efficiency increases monotonically as a function of the
proportion of outstanding voters or cumulative time, the
relative efficiency of voting systems varies.
For example, Figure 1 shows that the OPOV system is
most ERCO-efficient when 75% of the voters have
homogeneous preferences. As the proportion ofoutstanding voters declines, the probability of producing
an ERCO increase rapidly so that ERCO efficiency
exceeds .95 even when only half of the votes have been
received. Under the same conditions, the AV and
Copeland display an overlapping, less efficient ERCO
production pattern. Both of these voting systems are
much less ERCO efficient than OPOV even when the
proportion of outstanding voters approaches zero.
Figure 1Homogeneous Results
based on Votes Collected
In this bimodal culture, Figure 2 shows that making the
preferences of 75% of the sensors heterogeneous makes
Copeland voting, not OPOV, most ERCO efficient.
However Copeland votings ERCO efficiency increases
more slowly and achieves a lower maximum than the
OPOV system does (in Figure 1) when preferences arehomogeneous. In Figure 2, with 50% of the voters
outstanding, Copeland voting is 80% ERCO efficient and
only reaches a maximum of .9 ERCO efficiency.
Figure 2Heterogeneous Results
based on Votes Collected
Under these conditions, the OPOV and AV systems are
much less ERCO efficient and display a relatively flat,
overlapping pattern of ERCO production once 10% of
the outstanding votes have been collected.
Figures 3 and 4 present similar contrasts when
preferences in this bimodal culture become more
heterogeneous.
Figure 3Homogenous Results based on Time
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In Figure 3, when preferences are homogeneous,
OPOVs ERCO efficiency closely approaches a
maximum efficiency of more than .95 when only 250 out
of 500 seconds have elapsed. In contrast, AV and
Copeland voting display an overlapping pattern of ERCO
efficiency that increases slowly and produces a
maximum ERCO efficiency that is approximately 30%
less ERCO efficient than the OPOV maximum.
Figure 4Heterogeneous Results based on Time
In Figure 4, preferences are heterogeneous and the
Copeland method is most ERCO efficient. However the
rate of change in ERCO efficiency is slower and the
maximum ERCO efficiency is lower for Copeland voting
than they are for OPOV when preferences are
homogeneous. AV and OPOV display the same
overlapping, less-efficient, and flat ERCO production
pattern.
4. Discussion
ERCO efficiency can augment decision support forsensors by making it possible to predict how much(voting) information to collect or how long to wait toinfer that the collective inference at any point in adecision making process is actionable.
At the beginning of a sensor collective decision, C2 candetermine how long to wait or how many votes to collect
before taking action. ERCO efficiency analysis gives C2an information advantage that can be used to takeevasive action, launch a neutralizing counterattack, ordispatch first responders to mitigate the effects of anattack.
During an attack, C2 can obtain on-demandintelligence about the implications of waiting longer tomake a decision or collecting more information beforemaking an inference. ERCO-based analysis may revealif to wait for more votes to be received or time to pass orhow much longer to wait or how many more votes must
be collected to reach a distributed inference about thenumber of vehicles in the convoy.
.1 Tradeoffs among Voting Systems
In addition to revealing information about how long towait and how much information to collect beforereaching a distributed inference, ERCO analysis drawsour attention to tradeoffs between voting systems andwaiting and information collection.
Since voting systems answer different questions about
the same data set, choosing a voting system depends onwhat C2 wants to learn from the fusion process. In ourscenario, for instance, if C2s goal is only to learn whichof the five choices in the convoy assessment situation themost frequently top-rated choice is in the shortest
possible time, then, for example, the ERCO results inFigures 3 can be used with the OPOV results to reach anERCO inference that meets the time constraint. Forinstance, C2 might set a time to decide of 200 secondsinto the decision making process to achieve a high (.95)level of confidence.
However, if C2 wants to know more about thecollective assessment of the number of convoy vehicles,Figure 3 might be used to derive additional insights. For
instance, if C2 wants to know how much more each ofthe five choices was preferred to every other choice, thenFigure 3 would be used to take account of the Copelandresults to verify the results derived from the OPOV
pattern. In our scenario, the Copeland system isapproximately 30% less ERCO-efficient than the OPOVsystem, does not become significantly more ERCO-efficient as more time passes or more votes are collected,and displays volatility.. For these reasons, C2 mightdiscount the value of gaining a second opinion based onCopeland voting and consider the AV results. So C2might wait another 50 or 60 seconds to check the resultsfor AV that produces higher ERCO efficiency than can bederived from Copeland voting.
5.2 Further Research
The scenario investigated in this paper illustrates the
potential usefulness of ERCO analysis in providing
collective decision support when the network
environment includes imperfections in sensor decision
making and network communication channels. The
results of this scenario will be compared to those ERCO
efficiencies produced when a) sensors are assumed to be
perfect and communications channels are imperfect and
b) sensors are imperfect and communications channelsare perfect.
ERCO production is also being studied for peer-to-peer
scenarios and for situations in which decision tasks are
multi-dimensional. In convoy assessment task, for
example, additional dimensionality would be added by
asking about other attributes of the convoy (e.g., vehicle
shape, color, etc.) in addition to number.
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As probability results are developed for a variety of
ERCO scenarios, analytic models will be developed to
describe the effects of increasing or decreasing the
number of sensors and introducing periodic signal
interruptions into the fusion process. In addition,
situations in which the number of sensors is not known
will be investigated.
Concurrently, empirical tests will be conducted in
wireless sensor test beds.
* I would like to thank Russ Ovans and anonymous
reviewers for their comments on an earlier draft of this
paper.
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