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back to article Sheila's Fails? The statistics of biological risk

Yesterday’s ruling by the European Courts may have stirred the general public to a wide-ranging and not altogether informed debate on the issues of gender discrimination. Less obvious, but in the long run more serious, is the fundamental challenge it poses to the way in which two pillars of the establishment – the financial …

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Citation Required

I seem to recall hearing somewhere (yes, vague I know) that the reason women have statistically fewer accidents is more to do with miles driven than the quality of their driving.

Allegedly men tend to do more miles on average.

More miles = more exposure to other road users = greater chance of an accident.

This sounds believable if you simply assume that in spite of many years of women striving for equality that men are more likely to be the "bread winners" thus are more likely to have a driven commute of significant length.

That said, from my own anecdotal evidence, most of the people who behave like wankers on the road seem to be blokes. But then again most recent person I had to beep at for nearly causing me to be in an accident (by crossing a junction, across my path, when only the protected left turn light was green) was a bird.

My point? Not really sure.

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Correlation vs causation

...is the problem.

As far as an insurer goes, correlation is enough to indicate a probability, and as all decisions are based on probabilities, that's all that matters. Aggregated over a large enough population these probabilities are reflected in actual events.

But, as we all know, correlation does not imply causation. Just because an individual has a penis does not cause him to be a worse driver. This is where it becomes "unfair" - you're making an assumption that you can apply a property of the population as a whole to determine something about an individual, which is unfair if for whatever reason that individual doesn't match the population as a whole (some young male drivers are actually very careful, for instance, so it's unfair to tar them all with the same brush).

When it comes to other things, like annuities, maybe there is something inherent in the chromosomes that makes women live longer than men; if that causal link can be proven then it's fair enough to use that as a pricing differentiator.

But all this will fall on deaf ears, because the media will happily make you believe that just because X and Y occur together means X causes Y, or Y causes X, or less of Y will cause less of X, or whatever suits the headline.

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Grenade

Nicely misunderstood

It seems you read "Correlation does not imply causation" on the back of a matchbox and now quote that for everything without understanding it. The reality is, sex is a very good predictor of accident rates. That is a causal relationship. If it was just correlation without causation, sex would not be a good predictor. Of course, the distribution of accident rates is not narrow. There are many other predictors, many of which are not easy for the insurance company to measure. The variance caused by these other predictors mean that many people get tarred with the same brush potentially unfairly. However, do not be mistaken. Sex is an exceptionally good predictor of the cost to insure someone.

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Stop

Um, no.

Only men get testicular cancer. However, being male does not cause testicular cancer. In other words, "being male" and "having testicular cancer" are correlated.

Now swap "having testicular cancer" with "having more accidents" and you will see that it too is a correlation.

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Boffin

NO.

@AC "Nicely misunderstood.

"The reality is, sex is a very good predictor of accident rates. That is a causal relationship. If it was just correlation without causation, sex would not be a good predictor."

THIS STATEMENT IS ENTIRELY WRONG. A predictor is NOT a causal relationship. It is a mathematical relationship that simply states "There exists a given equation which, when applied to factor A will give an accurate estimate of factor B within a given level of statistical significance.

Correlation means that in the given dataset, factor A is a good mathematical predictor of factor B. A statistical analysis CANNOT GIVE YOU CAUSATION because it tests nothing but the mathematical relationship.

Only experimentation and logical inference can give you an indication of causation, and inference can only say that causation is likely.

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You may or may not have noted

That in my comment I said that sex is a very good PREDICTOR of accident rates. Not that it was merely correlated. You can measure correlation between 2 data sets. Then you can use that measured correlation to attempt to predict a future event. If your prediction is successful with statistics that show it is not just random chance, then you have developed strong statistical evidence of a causal relationship. You can also use those statistics to measure how strong the causal relationship is. If the correlation has occurred through random chance rather than causation, then the process of measuring how good the correlation was at predicting future results is a very good way to find that out.

The use of something in prediction is a key distinction between just measuring correlations. The reason for this is obvious. Causation requires a timeline - the initial thing must appropriately predict the thing you are trying to establish a causal relationship with. Putting your hand in a fire causes a burn, not the other way around, simply because the action of putting your hand in the fire precedes the burn. If you measure the correlation between burns and putting your hand in the fire you will get a high correlation. To establish which way causation runs, you can try to use one to predict the other. Does putting my hand in the fire predict a few seconds later that I have a burn; and does getting a burn predict a few seconds later that I will put my hand in the fire. Here you find that one thing predicts well, the other doesn't. Predictability is the key measure of whether a correlation is causal.

Remember of course, that the causal link between being male and having a higher cost of accidents is quite simple to describe. Young males have a higher level of testosterone than young females. Testosterone is the key hormone which distinguishes risk taking and confrontational emotions between people. Young males are more likely therefore to take risks and be confrontational. This leads to more dangerous accidents when driving. The causal relationship is strong and is evidenced very well through existing correlation being tested in a predictable way.

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Re: you may or may not have noted

You are still the one who is misunderstanding it.

As the back of the matchbox says: "Causation implies correlation, but correlation does not imply causation".

In other words, the fact that two events are correlated says nothing about whether one is the direct result of the other. It may indeed be the case (as in your hands in the fire example), or it may not be (as in the testicular cancer example).

I agree that the gender of a driver is a semi-reasonable indicator for the likelihood that they will have an accident, but that is still a correlation, not a causal relationship. As for high levels of testosterone in young males, that does not have a causal link to accidents. If it did, then _every_single_ young male who drove would have an accident. Since that isn't the case, it is only a correlation, albeit a strong correlation.

It should be clear why putting your (unprotected) hand in a fire and getting a burnt hand is causal - no-one can do the former without the latter happening.

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Boffin

Predictors

"Predictors. Predictors (also called independent or input variables) are variables used to predict or explain the value(s) of one or more dependent variables (also referred to as dependent or outcome variables)." [from http://www.statsoft.com/textbook/statistics-glossary/p/button/p/]

Note that there is NO mention of time or causality in that definition. That's because in statistics, predictors are not necessarily indicative of causal relationships. Terminology aside, what you're actually doing is not predictive; you're inferring that a correlation is a causal relationship through observation and logical induction, viz:

"[Observation:] Young males have a higher level of testosterone than young females. [Observation:] Testosterone is the key hormone which distinguishes risk taking and confrontational emotions between people. [Induction:] Young males are more likely therefore to take risks and be confrontational. [Induction:] This leads to more dangerous accidents when driving."

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XKCD

I'd just like to say:

"I used to think correlation implied causation, but then I took a statistics class, and now I don't."

"Sounds like that class helped then."

"Well, maybe."

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I'm glad

...that others also see where I'm coming from, even when people find it difficult to get their head around.

We can certainly show that being male is neither a necessary nor sufficient cause for car accidents (some women do have accidents, and some men never have accidents).

You might hypothesise that being male is, however, a contributory cause for car accidents. If there were a lack of correlation between being a man and having a car accident we would have disproved this hypothesis, but if we do observe a correlation that is still not sufficient to prove the hypothesis. There could still be other explanations for the observed correlation. Testosterone is one possibility. So then you'd have to go and build evidence for the causal link between testosterone levels and car accidents, and also a causal link between being a man and having high testosterone levels. And so on. This all requires a good deal of robust scientific research, and you'd need to be prepared to go down many blind alleys in the process (if, for instance, you found that the differences in testosterone levels in a sample of people were not sufficient to explain the difference in car accidents, you'd be left searching for another explanation for the correlation you first observed.)

The main point is that demonstrating a causal link requires a great deal more effort than just observing a correlation. It's a shame that more people, particularly journalists, don't appreciate the subtlety - if they did we might see fewer "X causes cancer" articles from the likes of the Daily Mail when actually often they are reporting on research where researchers have only demonstrated a correlation and possibly proposed a hypothesis.

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None of this exchange applies to insurance

Insurers are not interested in "causation" only in "correlation" as they are not attempting to determine why something happen only if it will happen. Insurers have therefore found a set of reliable predictors based on correlations in the data from the population they insure.

If they cannot use these predictors in the future they will a) seek predictors they can use and b) shorten their exposure to un-qualified risk by establishing the shortest period of insurance allowed. Expect to see rolling 30 day (7 day?) policies which reflect any actual (as a replacement for predicted) events in their premium. This limits the exposure to a single event, which need not be a major one, a speeding citation will cause your next month's (week's) premium to multiply 20 fold as you are now demonstrably a greater risk.

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As I said

in my first post.

This is why we have government regulation.

To an insurer, "fairness" doesn't matter. To an individual, it does.

As an individual it's fair to price for risk based on factors that can be demonstrated to actually cause risk, but to price based on factors that don't demonstrably cause risk but just happen to correlate to risk for a proportion of the population is not fair to a large number of people who are actually not a high risk but happen to match the risk factors.

The reason all of this is relevant is because the whole argument seems to be based on some kind of gut feeling of "it not being fair", without any explanation of why it's not fair, which is what this discussion has touched on.

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Boffin

Where does indirect end?

At what point does correlation of metric "X" with sex / race / disability / religeon or any other legally desciriminator-protected group equate to "indirect discrimination"?

Does it matter that such a correlation is causual or not, and how would anyone know?

Laws that attempt to restrict "bad" behaviour are horrid things to implement, even though we know why they are there.

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Coat

IT contracts

with solvency regulation, retail distribution review and now gender based pricing legislation all due for implementation it is going to be happy days for anyone working at retail life & pensions providers.

>> that's me getting my wallet to add in an extra 50 quid a month into my pension because my life annuity will be worth less.

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@bluesxman

"Allegedly men tend to do more miles on average.

More miles = more exposure to other road users = greater chance of an accident."

Quite probably correct ... that's one of the reasons why some of the coverage yesterday was suggesting we'd have to answer a lot more questions on the sort and amount of driving we do before we'll get a quote.

BTW, someone else mentioned Sheila's Wheels being discrimantory - actually I think that they will quote for men and in any case most articles I've seen about them indicate that women can normally get a better deal elsewhere! It probably relies on female customers assuming that it is (a) only insuring women and as a result (b) must be giving them a better deal!

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Stop

nope

but also crock. More miles = more experience = more chance to read the roads. I have driven close to 1million km. A middle aged gent driving less than 10km per year wouldnt have a 1/4 of my experience. I have never had an accident *that was my fault*. Ive been driven into a couple of times but neither my fault.

look at the statistics of idiots on the road. I would guess that the majority are inexperienced (white mondeo drivers excepted).

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Paris Hilton

Nominative Determinism?

Is Advocate General Juliane Kokott in her job because she is a tart? Kokott most likely comes from French "cocotte". See definition <a href="http://www.thefreedictionary.com/cocotte" target=_blank>cocotte</a>.

Our sweet Paris is of course a cocotte.

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Terminator

Missing the point of the article?

All the comments about male or female drivers being more costly to insure are missing the point of the article.

The ruling says that insurance companies are not allowed to exhibit gender bias, so simply asking if you are male or female is not the only restriction.

If little yellow cars are more often driven by women then the insurance company is no longer allowed to ask if you drive a little yellow car.

If there are other clustered attributes that discriminate then they also must be excluded.

If men have more costly accidents then they may no longer be able to ask the cost of your accidents.

If women have a higher frequency then they may no longer be able to ask the date of your accidents.

Same with other traffic offences.

So in summary, the logical conclusion is the if you drive a car you must pay a flat premium.

I for one welcome our existing overload's new tax on driving.

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Joke

25 years of driving

And my wife's never had a car accident...

Mind you, she's seen plenty in the rear view mirror as she's been swerving all over the road whilst putting her lipstick on.

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Does this affect the age sensistivity of life insurance ?

As above.

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Flame

What are you talking about?

"On the surface, this was a victory for equality, a defeat for the insurers"

I don't know what surface you're looking at but to me it's a blatantly unfair piece of politically-correct ruling in the face of reality. Sexist claptrap by unelected and unaccountable morons in fancy dress. Screw the lot of them.

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Here, here!

Don't hold back, tell us what you really think.

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Biological vs statistical

I seem to have missed the point on the confusion about the biology bit (I honestly have, no sarcasm). The statement that accident rates link to gender does not related to a biological difference seems very clear to me. She is saying that there is no medical cause for a man or a woman crashing more than the other. So my being male, in itself, does not make me more likely to crash (medically).

From this I assume she has concluded that there is no reason to assume that the statistic is a valid measure. If you mined your data enough you might be able to find a stat that said that people that liked apples are more likely to crash. The reason there is such abundant data on gender is that we all have one. The fact that data is skewed in favour of one group does not mean that the gender caused it (hence previous comments from people about causal links).

You could argue that the fact we have so much data and the result is not 50 - 50 does imply the measure is useful. Then again you would also say "apples make you more likely to crash" if we had enough data on that. you can cut your data in so many dimensions that you might get a significant weighting from any number of groups, it doesn't mean you're right, just that you might have over-mined your data.

This of course breaks down in the field when insurers find themselves paying out more to men than women. However I cannot (reasonably) change the fact I am male any more than I can change the fact I am white, however one is not allowed, one is (soon to be was). The insurers will need to look harder for a stat I can control that helps capture the risk

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@Will 28

>>"The insurers will need to look harder for a stat I can control that helps capture the risk"

Why shouldn't they be allowed to include things you *can't* control, if those things are good predictors of risk?

If someone was cack-handed and easily distracted (whatever the PC terms for those things might be), surely it'd be fair to charge them more if they're a higher accident risk, whether they can change their behaviour or not, whether their behaviours were labelled 'disabilities' or not, and whether there's any correlation with gender or not?

If driver A was highly aggressive, but could become a much safer driver if they went on a suitable course, and driver B was highly aggressive but wasn't changeable, would it be fair to charge driver A a higher premium if they'd hadn't been on the course, but unfair to charge driver B any extra for being a higher risk?

>>"However I cannot (reasonably) change the fact I am male any more than I can change the fact I am white, however one is not allowed, one is (soon to be was)."

Well, I guess as long as where people live has significant correlation with ethnicity, had one or other minority been a particularly good or bad risk, that might well be reflected to an extent in geographically-based pricing even in the absence of any ethnicity questions in the insurance application.

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Joke

I protest

As a left handed person at your use of the derogatory term "cack handed", everyone knows* left handed drivers have fewer accidents.

*this may not be true

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Why not?

Why not base the insurance premium on average distance travelled per annum?

Why do I suggest this? Thats because female drivers are only less likely to have an accident in a given time period, not in a given amount of geographical distance covered. When you consider distance, the effects change. Under 20, males are about 20% more likely to crash than a female, 20-35 there is no difference, and over 35 the female drivers are statistically more likely to crash in any given distance.

Surely this would be fairer, men who on average travel less statistically have fewer crashes, and women who travel more statistically have more crashes. So wouldn't a system where you have bands based on average distance be fairer, to both genders?

How you would go about implementing it I honestly don't know.

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Anonymous Coward

@Crellin

"How you would go about implementing it I honestly don't know."

I believe Aviva already have a policy whereby they fit a tracker to your car. It measures how far you drive and when you drive (though not your speed). People who drive outside of rush-hour, or only to the shops and back can get much cheaper premiums.

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Badgers

There was talk of taking this further

There was talk of taking this idea even further, if you drive on risky roads your premium goes up, the only obvious problem would be if some 'dodgy' areas command higher premiums and they happen to have a large population of a certain minority then this would be considered indirect discrimination.

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Anonymous Coward

The obvious, naive answer would be

to take all incidents, tally the cost, add overhead margin, divide by number of insured, and that's your premium. No questions asked. The only way left for these respectable gamblers to compete would be on reducing the overhead, leaving their profit as a function of how efficient they are at settling and administration and stuff.

Of course, this won't happen. But ideally, it should. Equallity for all. Maybe I can call this initiative misguided on grounds of insisting on equal outcome, not equal opportunity, even when you (or at least a supposedly learned lawyer in an influential position ought to) know you'll never get it. The road to hell and all that.

I think we need to come off the notion that discrimination is a dirty word. If that's the case then the knob on metal detectors labeled "discriminator" maybe needs to be labeled "racist", too. And sold in packages with big warning labels announcing it to be an un-pc, racist device. This not because the phenomenon that we're trying to stamp out is any less bad, but because we're deluding ourselves as to what it is, really. So perhaps we'll need to find a more specific word instead of repurposing a generic word for some specific thing, obscuring just how specific that thing is, really.

The problem is discrimination humans on grounds that have no demonstratable bearing on the subject nor the results to the person. Refusing to serve people in a restaurant because of their skin colour or their sex is something most of us will agree is a silly notion. Refusing to cast a white woman for a film role that calls for a black man is, OTOH, defensible. Even if hollywood script writers have this nasty habit of doing unspeakable things to their source material. But I digress.

The thing is, this shutting out our fellow human on some silly criterion --And I'll readily admit I have tendencies just as bad that sometimes conciously have to be kept in check; I'm just as fallible a human as (most of) the rest of us.-- is a social mechanism that might even be baked into our "clannish" genes; there's evidence that people without a certain gene also lack the tendency.

The Advocate General probably was after this disguised as a "valid" statistical technique, just like the measuring of scalps relating to race and religion turned out to be so much scientific bunk. But I think I'll agree she has overdone it a bit, as there are good arguments for proclaiming the statistical techniques to not having risen out of the social tendency.

That all needn't necessarily validate the statistical techniques --though for better or for worse they've been in use for a while and are generally accepted in the industry-- but at least would invalidate the presupposition that they need to be hit with the "anti-discrimiation" banhammer.

I think dear ms. Advocate General has some explaining to do.

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What is Needed

In the United States, it is impossible to purchase private health insurance. The only way you can get private health insurance is as a job benefit, although there is a legislated program called COBRA which allows you to keep your employment health insurance, if you pay for it yourself, after you lose your job.

Why is it impossible? Because several American states had the bright idea of forbidding health insurers from discriminating against people because they were HIV-positive.

The purchase of insurance is a private transaction between one person seeking insurance and an insurance company, and so the premiums charged should be based on as accurate an assessment of that person's risk as possible, based on all available information.

Any equalization or redistribution between people with different levels of risk needs to be done by the government through tax-supported programs. Because people don't have to buy insurance, attempting to set unrealistic insurance premiums by law will just destroy the form of insurance affected - if premiums are equal for everyone by law, only members of the highest-risk group will purchase insurance, because the premiums will rise to match their risk.

People shouldn't be discriminated against because of unfounded prejudices. Insurance companies following sound standards of actuarial practice aren't basing their premiums on irrational bigotry, and so insurance premiums should not be subject to any anti-discrimination laws, provided other laws requiring sound actuarial practice are complied with.

Common sense needs to be allowed to win out over ideology.

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What a load of bollocks

http://www.bcbsnc.com/content/plans/individuals/index.htm

is the URL of one of the many private health insurers in the US. It is complicated and expensive but it is readily available.

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Anonymous Coward

Turned down

After I changed car from one family estate to another family estate my existing insurers would not re-insure me. No idea why but there you go. Presumably insurers could simply not decline to insure <insert high risk group> without having to state why? How would anybody know. Sheila's Wheels by stealth if you like.

It's not like they have to publish a list of their clients...

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WTF?

If this makes it much further...

Then by the time I'm old, we'll be able to claim age discrimination so I can get myself medical insurance for the price of a twenty year old (despite plenty of evidence that I'm more likely to conk out expensively).

But I'm not stupid... what this means is a twenty year old will be able to get medical for the same price as an OAP...

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Stop

Madness!

Let's put aside all the debate around statistics for a minute. I think legislators need to step back and think, very carefully, about what anti-discriminatory legislation is supposed to achieve. The ECJ can only interpret the laws as they are worded and this is what they have done.

To my mind sexual discrimination (and racial and age discrimination) legislation is supposed to promote equality of opportunity and combat prejudice but I believe it should stop short of requiring that men and women be treated in exactly the same way. Incidentally, by the same token, I believe that this should also mean that so called 'positive discrimination' be outlawed.

When the insurance business applies statistical probabilities (rightly or wrongly, I'm not getting into that argument) to determine the likelihood of a given person being involved in an accident (and the likely cost of that accident) they are not being discriminatory. They are attempting to make an informed decision based on purely mathematical analysis. As long as Sheila's Wheels or Saga insurance will quote for men or for younger drivers respectively I don't see why they shouldn't be allowed to do this, as long as those factors can be shown to be statistically significant.

The policy intention of discrimination legislation should be to produce fair treatment for all, not to interfere with purely commercial operations that just happen to use demographics - as long as all demographics are catered for.

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Stop

positive discrimination

positive discrimination is already outlawed

The law does not recognize positive discrimination only discrimination. If anyone is discriminated against, male, female, black or white, they can take legal action against the offender.

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Enlighten me...

I seem to recall a fuss about Labour filling a quota of parliamentary candidates with female representatives. Didn't the Met also have some kind of positive discrimination policy? Has this kind of thing since been outlawed?

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Delibrately misusing the act

The way this is being misused would also lead to all drivers paying the same regardless of age, location, convictions etc.

Someone scoring points in the EU here I think.

In the end we would all lose through this.

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No end to this...

"Ultimately, that is the real issue for insurers. They can’t simply exclude inner city areas from insurance, because in today’s UK that would almost certainly result in a degree of indirect racial discrimination."

How is this different, in principle, from charging different rates for different postcodes? It's surely just a more extreme version. Those paying a higher premium for being in an inner city area might also claim that they are being indirectly discriminated against. If so, would only a member of an ethnic minority be able to claim such discrimination?

A can of worms indeed.

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Anonymous Coward

No problem for the smart insurer

sheilas wheels insurance WILL cover males but just look at the website - lurid pink "insurance designed with women in mind" handbag cover included. That's going to put a lot of blokes off.

Going forward they'll presumably have to change their rates for the boys but they don't discriminate against but just target a particular demographic with their advertising. Similarly they might advertise in women's magazines but not in Nuts and Viz.

On the other hand the 18-25 lads will be giving themselves away with all those adaptations to their vehicles - lowering the suspension, installing under-body lights, replacing the back seats with a sub-woofer, sticking a chrome double exhaust extension on, getting spinning hubcaps. Many insurers already regard these as "notifiable modifications" that invalidate the insurance if not reported and they can weight the premium in response - so they just need to increase the weighting.

BTW my 18 yo lad (with Pass Plus) was quoted £9k insurance for a lowest group 998cc vehicle. Shopping around got it down to half that, agreeing to a tracker and no driving between 11pm and 6am got it halved again and a sex change would have saved another £1k (he drew the line at that though).

It has to be said that we're doing it wrong. An 18 yo lad on statutory minimum for a 40 hour week after tax and NI would get just enough to pay that original £9k insurance quote. Even the eventual reduced cost is around 25% of their annual income so of course they're going to buy (steal?) an old banger and drive without tax and insurance. Legal constraints on under 25s like no more than one under 25 passenger, zero alcohol tolerance, would help reduce young drivers accidents (about a quarter of road fatalities involve young drivers - that in itself is unacceptable and the effect on premiums is inevitable) The driver's self preservation instincts lead to reflex decisions that result in it being the passengers that die.

A pass in an optional second "advanced" test could be used as a basis to offer reduced insurance (like PassPlus was supposed to do but there is no formal test, it does little more than certifiy 6 hours additional driving lessons after passing the driving test.)

Maybe "age discrimination in insurance" will be the next target of the courts...

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type of car

I disagree that type of car could become protected on gender bounds.

As a man I drive a "womens" car (even the toyota yaris ads sell it as such ("her yaris")). I chose this car as it is cheap to insure (and has excellent fuel economy). I have free choice over the type of car and can make that choice, and probably by the fact I make that choice shows I am less likily to cause a high value claim caring more about cost than performance. Where I cannot change my gender to get cheaper insurance (I assume sex change does not matter to insureres?) I can change my car.

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Boffin

A number of people

still are posting the "I drive ten miles a year and pay more than my wife/girlfriend/SO who drives a million miles a year and has an accident every day!" And "But this man / woman / sloth is paying the same as..." And Insurers should look at the individuals risk.

Go back to reading the DM. You're lack of understanding of the insurance system is beginning to bore me.

Do you buy you shirts / shirts from a bespoke tailor?

No, you by them from a shop which sells to a large number of people. So you get a "STANDARD" item of clothing.

And just WHAT makes you think that insurance is any different? If you want a cheap insurance deal, you'll go to a company who sells to tens of thousands of people. You'll put up with not having "your" risk calculated for the sake of saving a few quid.

There are quite a lot of insurers who would just love to insure you PERSONALLY. But it will cost you.

Just like a made to measure suit will cost a lot more than the off the peg counterpart.

So, you have your choice go cheap and get an 'off the peg' deal. Go tailored just for you and pay through the nose for it. Your choice.

So now you can stop whinging that the insurers are cheating you, because THEY aren't assessing YOUR risk. Go to a respectable broker and They'll arrange insurance just for you.

Also men and women are different. I don't know why, but they are. If you feel that you must make the genders equal then start at the beginning. In the UK 1011 girls are born for every 1000 boys. Start with that. Get the birth rates equal. How are you going to sort that one out?

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