Taxation and Happiness.

Using separate sliders gives you no concept of a) the actual taxation level, which is a single percentile between 0 and 100, and b) the ratio by which the burden of taxation is distributed to resource production.  Putting all those pips on a single slider and naming the resources between them gives you a flat bar-graph similar to a pie chart.  More importantly, it holds its ratios when you try to adjust the aggregate effect (taxation percentage) using its separate slider, and indicates in an easy-to-read manner the non-participatory resources, relating them to the portion of taxation not received.  Special note:  if you move EVERY slider in your example two notches to the left, you do NOT preserve the distribution ratio of resource production lost.  The burden shifts more heavily onto the resources with sliders furthest to the right.  In essence, you might actually (for example) increase the amount of food lost instead of decreasing it, because when it is twice as far to the right as clay, then you need to move it twice as far to the left to preserve the ratio between food and clay.  And none of this tells you what you also want to know:  what is the taxation level?  To put it simply, two sliders is better than 7 or 8, and the complex slider does a better job of preserving implicit relationships while easing the amount of effort required to make accurate aggregate adjustments.  The multiple sliders also are less expressive in that they're constrained to integer values, whereas my version allows rational values (ratios between resources and the whole rather than final values).  The former would inject inaccuracy into desired balance by that means as well...no matter how well the user administers the sliders.

Ideas are never complicated in our minds.  Attempts to build or use them show us the error of our ways, and math is a shortcut to finding the complexity that we will have to face and avoid.

To your previous point, taxation is already based on population and not resource production, and that whole relationship is already intrinsic to the whole city system.  Everything I described about resource production lost being a taxation factor while actual income comes from taxation being a population factor is descriptive of the current system without any tampering.  It would be a very bad idea to completely overthrow a system that already works and works well.  Far too many things depend upon this balance throughout the game, and messing with optimization-based game mechanics is very dangerous.  To be honest, I think that underlying relationship between population, taxation, and production is already as good as it can be, whether it's complicated or not.  I'm just trying to trade away the exploits needed for large populations and high income (basically huge food deficits in "finished" cities) in exchange for more nuance in city management.

As it currently stands, people can have massive armies and gold stocks--and meet population requirements for their next city--by starving the population, yet the population never gets smaller nor the gold income reduced.  Instead, they should be able to re-balance their production so that the gold and population is still attainable, but not by fabricating it out of nothing.

HonoredMule wrote: But taxation also affects production, and negative production means that stockpiles are being consumed/sold/destroyed to satisfy your greed for coin.

You have to remember that taxation comes from population not production.  It's not mathematically valid to treat it as applied to production itself without vague and oft-petitioned math in the background translating the aggregation into a factor applied to population.  Nor should we want the role of population in taxation to become confused or hidden.  It's also rather unpleasant to adjust gold requirements by shifting 7 sliders together (even if they're locked together, you'll end up with shifting balance and total screwups when sliders hit the edge).

But taxation also affects production, and negative production means that stockpiles are being consumed/sold/destroyed to satisfy your greed for coin.  -540% is -75% applied to each of 7 resources.  But if you're going to redistribute that tradeoff, must account for the whole amount from all 7 resources.  There's nothing wrong with having percentiles exceeding 100 in abstract math, nor using negative percentiles--rather it's a convenience that better represents and greatly simplifies the act of shifting production-loss burdens from one resource to another while still accurately accounting for the full tradeoff.  Thinking in large negative percentages allows us to still see the direct relation between production loss and taxation, where all the relations are simple aggregation.  When the distribution of production loss gets altered we end up with more complicated factors than 7*1/7 = 1, but that can't be helped, and it's fairly intuitive if the user is provided graphical representation--especially an interactive one.

It occurs to me that there's still a serious exploit in my system.  For example, you could transfer all the taxation cost to your Mana income and then completely destroy your Mage Tower to achieve net loss of -(some big number)% * 0 = 0 mana income.  Therefore, the percentage would have to be applied against a minimum minimum value when raw income is less than that amount.  Research and Mana would be the two likely culprits, and I doubt anyone would try to minimize food income as that's totally contrary to what is generally the primary edict we're trying to follow with or without this kind of taxation structure--get high gold income without losing so much food.  But to be sure, the minimum would have to apply for every resource being taxed, and possibly scale the very same way that taxation distribution itself does (i.e. a resource shouldering the full burden has 7 times the minimum income against which resource loss is calculated.  However, I would also scale it according to the ratio of maximum base incomes each resource is capable of producing, and then also multiply by the number of plots at that city which produce said resource.  -540% of 500 Mana income (-2,750 Mana/h) is appropriately detrimental, but -540% of 500 Clay income at a city with 7 clay plots isn't nearly difficult enough to handle.  -540% of 7*500 Clay income = -18,900 Clay/h is more appropriate minimum loss for such a heavily unbalanced distribution of taxation on a single resource.


Edited by HonoredMule - 05 Oct 2010 at 20:47

Someone posted somewhere an idea to make taxation more adjustable, using a 4-corner graph to specify the balance.  However, taxation occurs against population, not resources, and then affects 7 resources, not 4.  I think a better idea would be to introduce a new research item available only very late in the game, that allows players to distribute the cost of taxation using a single slider with 6 points on it, and appropriately cripple cities that don't feed their population.

The existing taxation/production sliders would still determine how much money is gained, that gold = 4*population*taxation translates back to 7/4*delta from 25% taxation.  So at 100% taxation and 25% production, there's 7*75% production loss to go around (i.e. 75% per resource affected by taxation, for the same 25% production per resource as normal).  However, that's a total of 525% production loss out of 700%, and players can shift the balance by moving the nodes.  The space between slider nodes represents the slice of production loss assigned to that resource, but the total will always add up to the full amount that must be removed.  It sounds confusing in textual description, but it's graphically quite straightforward and intuitive...just like slicing up a pie chart (which could be used instead, but would be more complicated to code and more difficult to manipulate when making tax adjustments).

Now here's the important part:  If a resource hits 0 and is at negative income, the population becomes unhappy/inefficient and taxation income reduces by 1/8th but the effect of taxation upon that resource continues.  This happens regardless of whether the city has the new technology researched.  What's more, for every increment of negative income on that empty resource equivalent to some percentage* of  pre-taxed production, gold income drops another 1/8th until hitting 0.  Starving peasants don't pay taxes.

*the appropriate percentage can be tweaked to find the right balance of cost, but for example's sake we'll use 20%.  The amount actually chosen should be such that any attempt to shift even half of taxation's cost to an empty resource results in total loss of gold income and maximum penalty to city happiness.

Example:  City "Sparta" has 1600 food income before taxation, and is being taxed at 100%, reducing income to 400 food/hour.  Sparta also has a population of 1360 for an aggregate food income of -960 food/hour.  When food runs out, Sparta will lose 4/8ths of its gold income, because -960 = -320 * 3 plus a remainder of 0.   In other words, each increment of negative food income equivalent to 20% of pre-taxation food income (or 320 food/hour) results in 1/7th loss of gold income, and any negative remainder results in another 1/7th loss.  If population increases to 1361, gold income drops to 3/8ths of taxation, and food income drops to -961.  Remember, of course, that the city can still maintain -961 food/hour and get the full benefit of taxation so long as another city keeps Sparta supplied with food.

As a result of this mechanic, it becomes no longer possible for high population cities to just build up long work queues and then run out of food and maintain 100% taxation, unless the tradeoff in food and other resources is an expense actually paid.  However, the ability to better distribute the burden of taxation allows cities to still and even better specialize while playing a balancing act between maximum output and danger of "riots" or however else you'd like to describe lost income (perhaps with a different name for each additional 8th lost: 1/8) worried, 2/8) pinching pennies, 3/8) discontent, 4/8) grumbling in the streets, 5/8) staging protests, 6/8) rioting in the streets, 7/8) revolting, 8/8) civil war.  One could then attach other damages to the extreme levels, such as troop and commander deaths, or destruction of building levels at the extreme end of things.  If you can shift all that lost output to your 7-plot resource, mana, and surplus research, you can still achieve positive results as extreme as current "exploity" behavior, but no longer without risk or trading off against output needed for maintaining sovereign claims and funding continued equipment production.

Then, after all this, if you still want the ability to influence happiness (having now given it a meaning that rises out of real circumstances and entails real consequences), you can now add new capabilities that provide a positive modifier to happiness, such as giving away free beer at some set rate.  Now, if for example you maintain two increments of free beer supply, your gold income/city happiness permanently has a "margin of forgiveness" equivalent to 2/8.  So, your negative resource income must be equivalent to 10 increments of 1/8th before gold income is 0 and the city plunges into civil war.  And at 2 such increments, you can still maintain full gold income and a perfectly happy city despite there being a marginal shortage of some basic resource.