# Example 935 — The option nobody chose changed what they chose `the_option_nobody_chose_changed_what_they_chose.eml` - A menu offers a small and a large; a medium is added that almost nobody buys; and sales of the large double. Every count is real and the medium really was chosen by almost no one. What an option nobody chooses does to the choice is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A menu offers a # small and a large; a medium is added that almost nobody buys; and sales of # the large double. Every count is real and the medium really was chosen by # almost no one. What an option nobody chooses does to the choice is computed # below. # # The experiment is careful. The two menus were shown to the same kind of # customers; the counts are real; the medium's own sales are honestly near # zero; and the intent is exactly 'did the medium matter'. # # The medium is priced almost like the large and is worse than it, so it makes # the large look like the obvious deal - an option that wins no choices moves # the choices, because people compare, they do not rate. 1000 => customers_per_menu 700 => small_chosen_two_options 300 => large_chosen_two_options 400 => small_chosen_three_options 0 => medium_chosen_three_options 600 => large_chosen_three_options 3 => price_small 7 => price_large int(large_chosen_two_options * 10000 / customers_per_menu) => large_share_without_the_medium_per_myriad int(large_chosen_three_options * 10000 / customers_per_menu) => large_share_with_the_medium_per_myriad large_share_with_the_medium_per_myriad - large_share_without_the_medium_per_myriad => share_moved_by_an_option_nobody_chose_per_myriad small_chosen_two_options * price_small + large_chosen_two_options * price_large => revenue_two_options small_chosen_three_options * price_small + large_chosen_three_options * price_large => revenue_three_options revenue_three_options - revenue_two_options => revenue_added_by_the_unchosen_option "menu of two : small " + str(small_chosen_two_options) + ", large " + str(large_chosen_two_options) ^0 "menu of three : small " + str(small_chosen_three_options) + ", medium " + str(medium_chosen_three_options) + ", large " + str(large_chosen_three_options) ^0 "" ^0 "large share, two options : " + str(large_share_without_the_medium_per_myriad) + " per ten thousand" ^0 "large share, three options : " + str(large_share_with_the_medium_per_myriad) + " per ten thousand" ^0 "share moved by an option nobody chose : " + str(share_moved_by_an_option_nobody_chose_per_myriad) + " per ten thousand" ^0 "revenue, two options : " + str(revenue_two_options) ^0 "revenue, three options : " + str(revenue_three_options) + ", " + str(revenue_added_by_the_unchosen_option) + " more" ^0 "" ^0 # ---- what the experiment verified ---- "the menu test" ^0 " customers : the same kind, two menus" ^0 " counts : real" ^0 " the medium's own sales : honestly " + str(medium_chosen_three_options) ^0 " intent : did the medium matter" ^0 " counts misattributed : 0" ^0 " verdict : NOBODY BOUGHT THE MEDIUM" ^0 "" ^0 " counting the medium's own sales honestly is the part" ^0 " done right here, and it is why " + str(medium_chosen_three_options) + " really is how many" ^0 " people chose it" ^0 "" ^0 # ---- what an unchosen option does ---- "comparison, not rating" ^0 " the model in the plan : each option has a value, people" ^0 " pick the highest, an unpicked option is irrelevant" ^0 " what people do : compare the options in front of them" ^0 " the medium : almost the large's price for less than the" ^0 " large - a foil that makes the large the clear win" ^0 " so the large : " + str(large_share_without_the_medium_per_myriad) + " to " + str(large_share_with_the_medium_per_myriad) + " per ten thousand, with the foil" ^0 " itself chosen " + str(medium_chosen_three_options) + " times" ^0 " kin to the spoiler in an election : an alternative that" ^0 " cannot win changes who does" ^0 "" ^0 # ---- what the seller got ---- "the outcome" ^0 " option added : one that sells " + str(medium_chosen_three_options) ^0 " revenue change : " + str(revenue_added_by_the_unchosen_option) ^0 " is any count wrong : no" ^0 " is an unchosen option irrelevant : no; it is the ruler the" ^0 " other options are measured with" ^0 "" ^0 # ---- null control ---- # The same customers offered the two-option menu and a three-option menu whose # third option is not dominated (a genuinely different item), so no foil. 300 => nc_large_share_two_options_per_myriad 600 => nc_large_share_with_a_dominated_medium_per_myriad 310 => nc_large_share_with_an_undominated_third_option_per_myriad "null control - add a third option that is not a foil" ^0 " large share, two options : " + str(nc_large_share_two_options_per_myriad) + " per ten thousand" ^0 " large share, dominated medium added : " + str(nc_large_share_with_a_dominated_medium_per_myriad) + " per ten thousand" ^0 " large share, undominated third option added : " + str(nc_large_share_with_an_undominated_third_option_per_myriad) + " per ten thousand" ^0 " no price and no customer changed; the third option stopped" ^0 " being a yardstick for the large" ^0 "" ^0 # ---- the rule ---- "what an honest count of the medium's sales guarantees" ^0 " almost nobody chose the medium : exactly, real counts" ^0 " the medium did not matter : not addressed; people choose" ^0 " by comparison, and the dominated medium moved the large" ^0 " from " + str(large_share_without_the_medium_per_myriad) + " to " + str(large_share_with_the_medium_per_myriad) + " per ten thousand while winning " + str(medium_chosen_three_options) ^0 "" ^0 "a choice is made among the options present, not from a private ranking; an" ^0 "option nobody takes can still be the one everybody measures against, and" ^0 "its influence is invisible in exactly the column where it was counted" ^0 "" ^0 "The medium sold " + str(medium_chosen_three_options) + " - honestly counted. But people compare rather than rate, and" ^0 "a dominated medium makes the large the clear deal: its share went from " + str(large_share_without_the_medium_per_myriad) ^0 "to " + str(large_share_with_the_medium_per_myriad) + " per ten thousand, " + str(revenue_added_by_the_unchosen_option) + " more revenue from an option that won nothing," ^0 "until the third option was one that stood on its own." ^0 ``` ## Python (deterministic transpilation) ```python customers_per_menu = 1000 small_chosen_two_options = 700 large_chosen_two_options = 300 small_chosen_three_options = 400 medium_chosen_three_options = 0 large_chosen_three_options = 600 price_small = 3 price_large = 7 large_share_without_the_medium_per_myriad = int(large_chosen_two_options * 10000 / customers_per_menu) large_share_with_the_medium_per_myriad = int(large_chosen_three_options * 10000 / customers_per_menu) share_moved_by_an_option_nobody_chose_per_myriad = large_share_with_the_medium_per_myriad - large_share_without_the_medium_per_myriad revenue_two_options = small_chosen_two_options * price_small + large_chosen_two_options * price_large revenue_three_options = small_chosen_three_options * price_small + large_chosen_three_options * price_large revenue_added_by_the_unchosen_option = revenue_three_options - revenue_two_options print("menu of two : small " + str(small_chosen_two_options) + ", large " + str(large_chosen_two_options)) print("menu of three : small " + str(small_chosen_three_options) + ", medium " + str(medium_chosen_three_options) + ", large " + str(large_chosen_three_options)) print("") print("large share, two options : " + str(large_share_without_the_medium_per_myriad) + " per ten thousand") print("large share, three options : " + str(large_share_with_the_medium_per_myriad) + " per ten thousand") print("share moved by an option nobody chose : " + str(share_moved_by_an_option_nobody_chose_per_myriad) + " per ten thousand") print("revenue, two options : " + str(revenue_two_options)) print("revenue, three options : " + str(revenue_three_options) + ", " + str(revenue_added_by_the_unchosen_option) + " more") print("") print("the menu test") print(" customers : the same kind, two menus") print(" counts : real") print(" the medium's own sales : honestly " + str(medium_chosen_three_options)) print(" intent : did the medium matter") print(" counts misattributed : 0") print(" verdict : NOBODY BOUGHT THE MEDIUM") print("") print(" counting the medium's own sales honestly is the part") print(" done right here, and it is why " + str(medium_chosen_three_options) + " really is how many") print(" people chose it") print("") print("comparison, not rating") print(" the model in the plan : each option has a value, people") print(" pick the highest, an unpicked option is irrelevant") print(" what people do : compare the options in front of them") print(" the medium : almost the large's price for less than the") print(" large - a foil that makes the large the clear win") print(" so the large : " + str(large_share_without_the_medium_per_myriad) + " to " + str(large_share_with_the_medium_per_myriad) + " per ten thousand, with the foil") print(" itself chosen " + str(medium_chosen_three_options) + " times") print(" kin to the spoiler in an election : an alternative that") print(" cannot win changes who does") print("") print("the outcome") print(" option added : one that sells " + str(medium_chosen_three_options)) print(" revenue change : " + str(revenue_added_by_the_unchosen_option)) print(" is any count wrong : no") print(" is an unchosen option irrelevant : no; it is the ruler the") print(" other options are measured with") print("") nc_large_share_two_options_per_myriad = 300 nc_large_share_with_a_dominated_medium_per_myriad = 600 nc_large_share_with_an_undominated_third_option_per_myriad = 310 print("null control - add a third option that is not a foil") print(" large share, two options : " + str(nc_large_share_two_options_per_myriad) + " per ten thousand") print(" large share, dominated medium added : " + str(nc_large_share_with_a_dominated_medium_per_myriad) + " per ten thousand") print(" large share, undominated third option added : " + str(nc_large_share_with_an_undominated_third_option_per_myriad) + " per ten thousand") print(" no price and no customer changed; the third option stopped") print(" being a yardstick for the large") print("") print("what an honest count of the medium's sales guarantees") print(" almost nobody chose the medium : exactly, real counts") print(" the medium did not matter : not addressed; people choose") print(" by comparison, and the dominated medium moved the large") print(" from " + str(large_share_without_the_medium_per_myriad) + " to " + str(large_share_with_the_medium_per_myriad) + " per ten thousand while winning " + str(medium_chosen_three_options)) print("") print("a choice is made among the options present, not from a private ranking; an") print("option nobody takes can still be the one everybody measures against, and") print("its influence is invisible in exactly the column where it was counted") print("") print("The medium sold " + str(medium_chosen_three_options) + " - honestly counted. But people compare rather than rate, and") print("a dominated medium makes the large the clear deal: its share went from " + str(large_share_without_the_medium_per_myriad)) print("to " + str(large_share_with_the_medium_per_myriad) + " per ten thousand, " + str(revenue_added_by_the_unchosen_option) + " more revenue from an option that won nothing,") print("until the third option was one that stood on its own.") ``` ## stdout (executed) ```text menu of two : small 700, large 300 menu of three : small 400, medium 0, large 600 large share, two options : 3000 per ten thousand large share, three options : 6000 per ten thousand share moved by an option nobody chose : 3000 per ten thousand revenue, two options : 4200 revenue, three options : 5400, 1200 more the menu test customers : the same kind, two menus counts : real the medium's own sales : honestly 0 intent : did the medium matter counts misattributed : 0 verdict : NOBODY BOUGHT THE MEDIUM counting the medium's own sales honestly is the part done right here, and it is why 0 really is how many people chose it comparison, not rating the model in the plan : each option has a value, people pick the highest, an unpicked option is irrelevant what people do : compare the options in front of them the medium : almost the large's price for less than the large - a foil that makes the large the clear win so the large : 3000 to 6000 per ten thousand, with the foil itself chosen 0 times kin to the spoiler in an election : an alternative that cannot win changes who does the outcome option added : one that sells 0 revenue change : 1200 is any count wrong : no is an unchosen option irrelevant : no; it is the ruler the other options are measured with null control - add a third option that is not a foil large share, two options : 300 per ten thousand large share, dominated medium added : 600 per ten thousand large share, undominated third option added : 310 per ten thousand no price and no customer changed; the third option stopped being a yardstick for the large what an honest count of the medium's sales guarantees almost nobody chose the medium : exactly, real counts the medium did not matter : not addressed; people choose by comparison, and the dominated medium moved the large from 3000 to 6000 per ten thousand while winning 0 a choice is made among the options present, not from a private ranking; an option nobody takes can still be the one everybody measures against, and its influence is invisible in exactly the column where it was counted The medium sold 0 - honestly counted. But people compare rather than rate, and a dominated medium makes the large the clear deal: its share went from 3000 to 6000 per ten thousand, 1200 more revenue from an option that won nothing, until the third option was one that stood on its own. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done