Men versus Women Drivers

Christian Party

Men versus Women Drivers

	Per Traffic Safety Facts' "Vehicle Miles of Travel, 1975-1996" http://www-fars.nhtsa.dot.gov/www/cfm/library/rpt_info.cfm?index=Trends:Occupants&recordid=0 Americans drove passenger cars 1,478 billion miles in 1995.
	Per the "Early Results Report" of the Nationwide Personal Transportation Survery http://www-cta.ornl.gov/npts/1995/Doc/index.shtml men drive 65.3% or 965 billion and women drive 513 billion of those miles.
	Per Traffic Safety Facts' "Drivers Involvement in Crashes" from the FARS data base http://www-fars.nhtsa.dot.gov/www/cfm/library/rpt_info.cfm?index=People:Drivers&recordid=0 male drivers were involved in 2,418,799 fatal and injury crashes and female drivers were involved in 1,701,043, for a total of 4,119,842 drivers in approximately 2,059,921 accidents.
	The accident rate per one million miles driven for men is 2.5 and for women is 3.32 (33% higher).
	Per the NHTSA http://www.nhtsa.dot.gov/people/economic/ecomvc1994.html the economic cost of motor vehicle crashes in 1994 was $150 billion.

The higher probability that women will have an accident contributes to an increase in the accident rate for men. To determine exactly how much higher the accident rate for men is because of women drivers it is necessary to calculate the probability for both men and women to have an accident. If we let P_m be the probability that a man will have an auto accident, and P_fthat a woman will, then we have two equations and two variables. The total probability that a man will have an accident is the sum of his probability of having a single driver accident, the square of this probability to represent a two driver accident involving another man, and the P_m times P_f to represent a two driver accident involving a woman:

(P_m + P_m² + P_mP_f) x 965,000 million miles driven = 2,418,799 accidents

P_m + P_m² + P_mP_f= 2.5

The equation for women is similar:

(P_f + P_f² + P_mP_f) x 513,000 million miles driven = 1,701,043 accidents

P_f + P_f² + P_mP_f = 3.32

P_m = (3.32 - P_f - P_f²)/P_f

(3.32 - P_f- P_f²)/P_f + (11.0224 -6.64P_f - 5.64P_f² + 2P_f³ + P_f⁴ )/P_f² + 3.32 -P_f^-P_f² = 2.5

3.32P_f- P_f² - P_f² + 11.0224 -6.64P_f - 5.64P_f² + 2P_f³ + P_f⁴ + 3.32P_f^{2 -} P_f^{3 -}P_f^{4
= 2.5}P_f²

3.32P_f+ 5.82P_f² = 11.0224

P_f= 1.087 = Probability that a woman will have an auto accident

P_m= 0.213 = Probability that a man will have an auto accident

P_f= 5.1 x P_m

If all drivers were men who drove the 1,478 billion miles which are currently driven by both men and women, the total accident rate would be 0.26 accidents per million miles, for a total of 380,480 accidents:

(P_m + P_m²) x 1,478,000 = 380,480 accidents

If all drivers were women who drove the 1,478 billion miles which are currently driven by both men and women, the total accident rate would be 2.271 accidents per million miles, for a total of 3,352,945 accidents:

(P_f + P_f²) x 1,478,000 = 3,352,945 accidents

If only men drove today, accidents would decrease from 2,059,921 to 380,480 per year, a reduction of 81%. If only women drove, accidents would increase from 2,059,921 to 3,352,945 per year, a 63% increase and there would be 8.8 times as many accidents than if only men drove.

Women drivers are thus responsible for $121.5 billion of the $150 billion annual economic loss and 36,450 of the 45,000 lives lost each year to auto accidents.

A = Drinking men = 11 = A + A² + AB + AC + AD

B = Drinking women = 6 = B + B² + AB + AC + AD

C = Non-drinking men = 47 = C + C² + AC + AB + AD

D = Non-drinking women = 75 = D + D² + AD + BD + CD

B = (47 - C - C² - AC - AD)/A

D = (11 - A - A² - AB - AC)/A

A = (75 - D - D² - BD - CD)/D

B = (47 - C - C² - (75C - CD -CD² - BCD - C²D)/D - 75 - D - D² - BD - CD)/ (75 - D - D² - BD - CD)/D

B = (47D - CD - C²D - 75C - CD -CD² - BCD - C²D - 75D - D² - D³ - BD² - CD²)/ (75 - D - D² - BD - CD)

75B - BD - BD² - B²D - BCD = 47D - CD - C²D - 75C - CD -CD² - BCD - C²D - 75D - D² - D³ - BD² - CD²

75B - BD - 0BD² - B²D - 0BCD +28D +2CD +2C²D -75C +0CD² +D² +D³ = 0

75B - BD - B²D +28D +2CD +2C²D -75C +D² +D³ = 0

A² = (5625 - 150D - 149D² - 150DB +2D³ -150DC +2D²B + D⁴ +2D³B + 2D²C + 2D³C + D²B² +2D²BC +D²C²)/D²

11 = (75 - D - D² - BD - CD)/D + (5625 - 150D - 149D² - 150DB +2D³ -150DC +2D²B + D⁴ +2D³B + 2D²C + 2D³C + D²B² +2D²BC +D²C²)/D² + (75B - BD - BD² - B²D - BCD)/D + (75C - CD - CD² - CBD - C²D)/D + 75 - D - D² - BD - CD

11D² = 75D - D² - D³ - BD² - CD² + 5625 - 150D - 149D² - 150DB +2D³ -150DC +2D²B + D⁴ +2D³B + 2D²C + 2D³C + D²B² +2D²BC +D²C² + 75BD - BD² - BD³ - B²D² - BCD² + 75CD - CD² - CD³ - CBD² - C²D² + 75D² - D³ - D⁴ - BD³ - CD³